Sounds like they are having trouble adjusting to the new baby.Â
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At this age, prevention is key. Would leave two puppies alone with access to a pile of new leather shoes and hope for the best? I think you need to get better locks...pad locks with keys only you have, around your neck, or combination locks. I think you need to throw out anything you don't really truly NEED that they can use to cause damage. I think you need to toddler proof your house (yes, I know here, there are a lot of moms who group 3.5 into the childhood years, but for me, 5 was the end of the toddler years in terms of emotional maturity and communcative skills.) They cannot be trusted to be patient. They can not be trusted to exihibit self control. They cannot be trusted to not express their anger in violent and hideous ways. They can not be trusted to not do exactly as they want to do. It is up to us to limit the possibilities in reasonable ways.
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At least until they are a bit older.Â
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The bed situation could be solved by giving them sleeping bags instead of sheets and blankets.  They get rolled up and put away each morning, sort of like futon style, instead of being made, or you could sew the edges to the mattress with a simple whip stitch that could be removed when they are ready for real bedding . Or you could be mean, like my parents would have been which would have been...can't keep the blankets on the bed...you lose the blankets for a week. That seems unduly harsh, but it was effective to some degree...and in order to keep the blankets by being replaced with toys or clothes, the rule was simple: Anything left out after you leave a room is put away in the attic (which only my parents had access to, locked with a key on dad's Key Chain). If you leave it under a chair, on the stairs, on the kitchen table...it will be placed neatly in the finding spot until bed time. If it is not taken back by bed time, you will never see it again (until we moved out of the house...I kid you not! I found a half read book, a few dolls I'd always wondered what happened to...but really there wasn't that much...we learned the rule fast!), and it was not replaced with new stuff, either. You got new things when you out grew the old, or at Christmas and birthdays. That was it.Â
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For my family we are not quite as strict, but we do take away things that are left out, not forever, but for a day, then a week, then a month, then a year etc until they can handle the responsibility of playing with it nicely and putting it away. I got rid of all unwashable markers in the house except for one small sharpie on my key chain. We also put all paints and crayons away under lock and key and took them out only for long trips and special occassions.
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I don't have twins, just had ONE 3.5 year old boy, and he caused plenty of damage (still does) by himself.  Twins are notorious for conspiring even at very young ages to up the ante, so to speak. I would say the first step would be to separate them if possible.
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Or you could lock their bedrooms doors when you are finished making their beds. Bedrooms arent really for playing, anyway. Not at that age, if you ask me. I keep the play where I can see it at all times. The kitchen table, the living room....
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So let's say you have to take care of the baby (I am fascinated by the way how a teething accident -- actually I don't even know what that means -- could lead to a baby needing a bath so immediately you did not have time to give the twins breakfast...especially KNOWING how clever and sneaky they are when their needs are not being met. What in the world happened!?) perhaps you could enlist the help of one of them to test the water temp, or play peekaboo with baby while you bathe her, change her, etc? This at least removes the collaborative thinking element to their destruction. In this case, two brains are more devious than one.
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I think the thing to remember here is that although you have a new baby, they are still babies in many ways, too.  In fact their needs are going to often require even more immediate attention because unlike a baby they are capable of finding ways to meet their needs in very undesirable ways (expressing frustration through destruction, finding food in high up places, destroying what matters to you to get your attention...) The baby will probably be happy in your arms as long as she is dry and fed and in your arms or on your back, and even if she's not entirely happy, how long does it take to grab bite to eat? ( if the answer to that is more than 1 minute, then may I suggest the muffin tin snacking system...fill up at night or in the a.m., whenever you have time, fill each cup with their favorite things, leave at reaching level in the kitchen, or hand it to them when they are hungry between meals or as a quick meal in a pinch.) Ten minutes is forever for a 3 yo. 3 minutes feels like a lifetime.
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As for consequences? I think it's fair to ask them to help you clean up, (at least pre-wah before the chemicals are needed -- that way they can SEE the damage they have done, how it won't come out, and how hard you will have to work to clean it...) and meanwhile you can talk to them about how sad it makes you, and they can help brainstorm a restorative action to bring justice to the situation. Another obvious consequence is that they are no longer allowed out of your sight, during waking hours.
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FWIW, if you have a supply of high protein breakfast foods ready to grab and go this could really help their overall behavior throughout the day, power bars, boild eggs, smoothies ready made, yogurt cups, etc. Just a thought. Sometimes small changes in the diet can really have a huge impact. Sounds like you have a very typical UK home, in that there is a LOT of white starch in the house (bread, biscuits, crisps, etc) maybe think about reducing the wheat and processed carbs from the house and see what happens to their behavior. It's worth a shot!
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