Okay, first off, as a new poster to this particular forum and a long-time lurker on MDC (and just because it has to be said, just because someone doesn't have a lot of posts doesn't mean they don't read and pay attention to what goes on here), I have to admit that I'm a little afraid to post anything. Honestly, I have to admit, the OP seems to be a bit on the hostile side towards anyone who doesn't share her opinions, and I think maybe it should be said that the kind of hostility displayed may just scare people off, like myself, who really could use the support in unschooling with my kids, especially since we've had a number of problems as of late that have made it a LOT more challenging than usual. I've heard several unschooling moms say "public schools aren't the end of the world" and have even considered it myself when I felt that maybe I couldn't meet the needs of my kids, as much as I hate everything about public schools and seem to share a lot of the same views as the OP.
I hate to say it, I came to MDC after a friend of mine told me how welcoming, friendly, and caring everyone here was. She told me how there was very little drama and even less hostility. In my experience, many people here like to keep it that way. Instead of reacting to something that offends or upsets them, they just let it roll off their back. Thinking about it, this is a skill I've had to learn from the very start of my parenting journey. Sometimes it's just better to say, "That's interesting advice. I'll take that into consideration." Then just let it drop. Hostilities are meaningless if no one takes the bait.
That being said, I'm going to speak my mind and hope that I don't get pounced on because I'm just a "newbie" and my post count isn't high enough if my opinion isn't what wants to be heard...
From what I'm reading in all of this ISN'T a matter of unschooling versus school. It sounds like the huge problem here is a matter of discipline and boundaries. For example, if your daughter could respect your boundaries, she wouldn't have barged into the bathroom to start playing with everything while you're showering. She wouldn't be destructive (I think I read she cut up the couch? Or something at least) if she could learn to respect property that isn't hers. Whether you use formal and more traditional punishment and/or rewards or use unconditional parenting techniques, there still needs to be some way of communicating to your daughter that some of her actions are not acceptable.
Let's look at the bathroom incident. There are a number of places there where there is a recognizable need to put your foot down. First was her demand that you play a game with her, though that was fair well handled. The second was the point at which she entered the bathroom. The third was the point at which she started playing in the sink and filling the bin with water. It's not so much that I think your kid shouldn't want to play games with you, or that she shouldn't be allowed to play with water, but you stated a clear boundary, you needed 10 minutes to take a shower, and she walked all over it. The situation with the contact box and the water could be another of these situations depending on how you feel about it.
I'm not going to tell you how to correct the "behavioral" problems, but simply to point out that it's time to consider ways to help her to respect the needs of everyone around her and their property. She's old enough to understand concepts like your feelings, and to respect your feelings. She's also old enough that she can start learning to respect the property around you. While I can't tell you how to raise your kids, I can give you some examples from my daughter in similar situations, like wanting to set up all her toys in the hall outside my room because I was in the shower. We simply made it a rule that playing in the hall is not allowed because it's dangerous. Someone could get hurt stepping on or over the toys and it makes it hard to get out in the case of a fire. If she wanted to play with her toys, they belong out of narrow lanes of travel, like hallways. If I saw the toys there again, I would put them away until the end of the day. I figured it was better to put up with the temper tantrum that would ensue than the very real possibility that her younger brother or I could get hurt trying to get over or by them. When I caught her playing with scissors and cutting up things that were not hers to cut up, I informed her that she could only use scissors on her own things without permission. We had to set up a rule that she was no longer allowed to use scissors without permission. I tried as much as I could to sit down with her and help her come up with the problems of respecting the space and boundaries of those around her when she was bored, but it wasn't easy in those days because I was so burnt out with dealing with a child that did crazy things like unlock the door and sneak out of the house when I was preoccupied with something else at the time. It was pretty necessary given that in many cases she was either doing something that could pose a great danger to herself (like sneaking out of the house at 4 when there was a kidnapper known to be stalking in the area) or were destructive for the property around her. It's a matter of picking your battles, and focusing on what will keep her safe, not cost you a small fortune in things that need to be replaced because she destroys them, and trying to find enough personal space and peace that you can have enough energy for her needs.
I know this doesn't address the unschooling/homeschooling issue, but I don't think that's the only concern unless she doesn't do those things at all during the year that preschool is running, but from the sounds of it, that's not the case. That means there's something else going on. On top of helping her understand and respect the boundaries you need in your home for everyone's safety and sanity, you could also talk to her preschool teacher. Perhaps they have some advice on things that they do differently than you do at home. Perhaps it's because there are plenty of options for structured activities for her to do. Many preschools use time-out as a way to re-enforce following the rules. There could be any number of things that they're doing that help her engage in non-destructive activities and it's not just the socialization. That's a resource you have that I didn't with my daughter. She never went to preschool and only spent a short time in daycare while I was working. As a result, I had to figure it all out on my own.
From the sounds of it, you'll probably feel a lot better once you set up some boundaries in your house and some guidelines for respecting both other people and the things around her. Once we set that up with my daughter we had a lot less problems with her being destructive. Sure, she had her moments (though she had other reasons for that, like the absence of her father in her life), but for the most part, things started to flow much better around here. We chose to go with primarily unconditional parenting techniques, but given my boyfriend and I both have backgrounds very different than that, I'll admit that we've both slipped up more than we'd like. I started this before my boyfriend was even a part of our lives and we saw a miraculous change in my daughter. It took a couple months (not the weeks that I've heard other people tell me to expect a major change) but I found that I was able to take a shower, take out the trash, get the mail, and even cook Thanksgiving dinner without having to worry about my daughter getting bored and destructive because I wasn't there to provide her with the social interaction she wanted. We worked together to find what worked for her so that we could all co-exist more peacefully.
In a lot of ways, I understand where you're coming from. My family doesn't have a lot of money for activities. Waldorf style activities, while wonderful for my son, proved to be rather dull for my daughter and she lost interest pretty quick. We didn't have much options for stuff like that either. There wasn't much for kids in her age group when we first got here, and now it seems like the focus is still on the older set. Socialization at free things like play groups worked wonders for making sure she still had plenty of time with friends, but we haven't been able to attend them as much as we've liked because we're currently without a working vehicle. However, building this style of communication and the basis of respect and understanding that there are reasons I tell her I need or the family needs to work within the limitations we have has made this difficult time that much easier. I've never been one for harsh rules, strict discipline, and restrictive boundaries, but I think it's important for my kids to know that I'm much more capable of tending to their needs when I know that I can take a shower, make dinner, or do whatever I need on my own without having to worry about turning around to see the house destroyed or the kids climbing on the counters to get into the granola bars I'd put away for the co-op on Monday. It's nice to know I can sit down to read a chapter of my book or do a row or two of knitting without having them come up eight million times to ask questions. Having those little breaks to get things done while the kids are on their own, entertaining themselves and being respectful of their home and each other (usually...it's been hard since we've moved into a 2 bedroom temporarily) means I'm more available to meet their needs because I have the energy to do it. On top of that, learning to respect the needs and wishes of those around them will only help them grow into respectful and caring adults, so in my eyes, I'm really getting two things out of one. I was able to let my kids have alone time without worrying that their means of entertaining themselves would also mean being destructive, and I'm providing yet one more lesson to my kids about respect.