I'm sorry to hear that you are having such a rough time.
I know that sometimes you may not feel like going to a playgroup but why not do it for your child? Just sit there and be bored the entire time, at least your child will be having a great time. Also, there are a couple of main reasons why people don't "click" at the playgroups. (1) because they don't go enough (2) because it's not the right group. But seriously, I think #1 is the main one. I've been in numerous groups and sometimes it can be really hard to make friends with newbies when they only come once a month or once every two months, because sometimes us long-timers are a bit shy, too!! And since we've been in the group for ages, we get busy talking with all the friends we have made and sometimes forget to go out of our way to make friends with the new mamas, or even if we do, the new mama may not feel incredibly impressed by us immediately.
Just keep trying, please! I swear, joining a moms club saved my sanity so much that I feel every single stay-at-home parent should join and participate in playgroups and clubs as much as possible.
If you are convinced that the playgroup you are in is not for you, then try more groups.
Here's a list of Attachment Parenting International Groups in Texas:http://www.attachmentparenting.org/group/webtx.shtml
Here is a MOMS Club link, so you can find out what chapter would be for your area: http://www.momsclub.com/join.html
Click on your area to find some mom and child meetups.
If you are going to homeschool, or even just thinking about it, join one or two of your local homeschool groups. Try looking in your local free parenting magazines under the calendar and support group areas and join them.
Also, contact your nearest local library and make sure that you go every week to the free children's story time. For your 5 year old, there are sure to be free children's classes, too, fun educational activites, crafts and classes periodically. While your children has fun learning, doing and interacting, you can explore with her or sit there reading or chat with a few other moms who are sitting there with their children, too.
Once you meet some moms with children who seem to click or are similar ages to yours, then set up a day and host a playdate. If you don't want to have it at your home or in your yard, choose a local playground and invite 3-5 moms for a 2 hour playdate. If you do that once a week or every two weeks, it won't be long before your daughter starts making some friends, really starting to click with some of the children and chances are, you will click with some of their moms. When I did this, lo and behold, after a few weeks, some of the moms started hosting a Friday playdate themselves and inviting all of us. It was so great!!
One of the great things about clubs like MOMS Club is that most chapters have a monthly calendar and newsletter. What our chapter did was having a group activity every Tues and every Thursday. Sometimes it would be a field trip, usually free, but sometimes at a group rate, and we would all meet there. Usually every week there would be one playground get-together. Plus, once a month there would be a moms night out, where we would vote on what we wanted to do. Frequently it would be a night out for the moms, where we'd go to a restaurant or coffee house and eat appetizers or supper together. Sometimes it would be a paint-your-own-pottery night or a cooking club (potluck party) or a cheap manicure/pedicure at a local vocational college or a movie night at someone's house. These nights were such a great way to unwind and justr recharge a mama's mind and soul and a nice way to bond again, with other mamas. Usually, our moms night outs had anywhere from 10-16 mothers, so it wasn't hard to find a few mamas who you really got to know and enjoy, even if you didn't feel like you wanted to be best friends with everyone. Remember, all of the other mothers in that group are looking for new friends and/or friends for their children, exactly the same as you!
What I love about field trips and classes were that I felt no pressure to socialize with others. We would get a discounted (or free) group rate to fun local attractions that I might never have thought to go to, and my children and I could enjoy a fun and interesting activity. No pressure, no having to think of "what should we do" and just the fact that we were in a group meant that we could follow the lead of others and do what they did, or branch off a little and do what we chose.
Once I started getting into these groups, I delve even further, by getting involved in running a group or two, organizing events, coming up with ideas and even publishing newsletters and such. It was amazing how much fulfillment I got out of doing those seemingly mundane tasks. Truth is, I got to make the club into what I wanted it to be, and that was a great feeling. Plus, I felt like I had a purpose outside of being a Stay at home mommy and it was really good for my sanity. Really, really good. And it forced me to be more sociable than I was naturally inclined. Since I was on the board of the club, I needed to make sure I talked to every new person, introduced, tried to make them feel invited and comfy, and soon enough, I knew everyone and everyone knew me.
Though you might not want to do everything that I did, please do pick and choose and do as much as you can. I swear, if I were to stay home all the time, my children and I would not be very happy. Instead, we have a full and varied and busy, busy social life going out and doing things as often as we want. We get to pick and choose from our calendars and groups and can do things every day if we please and rarely be home, which we do sometimes, or we can stay home whenever we feel like it, because we want to and want to enjoy being at home, instead of because we have no other fun choices.
Good luck! Feel free to PM me if you want any more ideas or info. I tried to keep the above relatively brief...(not my forte, obviously!)