Mary, I think that some sessions with a counselor would really help you and will make these things so much easier for you. You don't want to keep your children from their activities because you're still carrying around baggage from your childhood, right? This is definitely the kind of thing you can be "coached" into improving. A good counselor who is skilled in this area would help you to bring up those old feelings of rejection and inadequacy (sp?) and process them so that you can let them go and would also help you with coping skills and a "script" for social situations.
I don't have social anxiety, but I'd rather give a speech in front of hundreds of people than walk into a party or social situation alone. The thing is, more people than you realize have trouble breaking the ice at these things. I remember when my kids were younger it seemed like when we went to school or sport functions, everyone was greeting each other like they were best friends. In reality, there was only a small percentage of people in any setting who were actual friends, they were just louder and more excited than the rest of us who were standing around feeling awkward. So here are some things that work for me:
1) When at all possible, I connect with a "buddy" before hand so that I don't walk into a social setting alone. Usually just a quick interaction. When going to the company holiday party, I'll ask a colleage "hey what time are you heading down to the party? 5:30? Great I'll swing by your cube and we can walk in together." For a sports or school function maybe a quick text: "hey are you going to X? OK great we'll see you there" or "do you want me to pick you up on the way? You know how crowded the parking gets at these things..."
2) Learn people's names. It's so much less awkward when you can smile, wave, and call out "hi Julie, how are you?" when walking in somewhere. And learn their kids' names. This is harder to do when they get older (I have 4 kids and they all play sports) but it's worth it. When you know who people and their kids are, you can initiate conversations like "wow that was a great play that Nate had earlier!" or "Annie did a beautiful job on that art project, what talent she has!" It's hard to resist someone complimenting your child.
3) Find a job to do - one of the first times that I met my husband's extended family when we were engaged was at his grandfather's funeral. We went to sit shiva at his grandmother's house. I knew very few people and they were all in a state of grief, so I went into the kitchen and helped with making sure that the ice buckets were full, refilled utensils and napkins, put more rolls out, etc. It gave the close family members time to spend with their guests and not worry about logisitics and in doing so, I got to quietly get to know the more distant relatives who were also helping out in the kitchen.
4) Have a script, a list of ice breakers for a variety of situations. Compliment someone's shoes or scarf, talk about the weather, or your local sports teams, or ask if they're doing anything fun this weekend. Ask who their child's teacher is, how their child has liked 1st grade (or soccer, or whatever). Trust that many people are feeling just as awkward as you and will welcome you breaking the ice first.
I hope some of the suggestions help and would definitely seek out the help of a trained counselor for this. It's an anxiety that is well worth conquering, for yourself and your kids!