anti-social 4y, personality or phase?

[Peony]

DD2 is the 2nd child, I'm pg with #4 so that gives you an idea of the line up.  She just does not want to play with other kids. It didn't use to be this way, but around her birthday last fall, I noticed a change. We tried this awesome little crunchy, playschool, nope. She does do gymnastics and dance, she always hangs back clinging to me and then will go off. Sometimes with more prodding then other times. Playdates are hit or miss, some times she might play after a while or other times she will sit there the whole time asking why that kid is in her house or wanting to go home. We go to open gym often, again very hit or miss. She might run around with friends or sit begging to go home, like today. 

It wouldn't be a big deal but she wants to play with other kids. DD1 is very social, has friends over and goes to their house and DD2 wants to come along or play with them. This morning she kept begging for a friend, wanted someone to play with so we go to open gym where two of her friends were there and she refused to play with anyone. Instead she is siting here watching a cartoon, happy as a clam, while I type this.  DD1 has always been the type that would play with anyone, and she is reserved but it didn't stop her having still having fun. DD2 is very particular. It seems like all the stars have to be aligned perfectly before she will even consider talking to another child. Sitting in the car by herself is something she would choose over playing some days. What gives? Anyone else have a child like this?

[Viola]

It could be a phase, although she might just generally be more introverted in general.  I vaguely remember my dd1 as a 4 year old being like this.  When she had her 4th birthday party, she was pretty antisocial and didn't want to play with the other kids.  She did end up going to preschool when she was 4, two days a week, and she didn't like it at first, but the teacher helped her befriend a new girl, and then she and that girl really liked each other.  She is 11 now and tends to have 1 or 2 friends, but she isn't as involved with all the groups of kids.

My 7 year old really doesn't seem to have any friends, at least not any that come and have playdates.  She likes to play with a 12 year old friend of dd1's, and they get along fairly well (usually when DD1 is reading a book or not playing with her own friend, LOL).  In general I think of DD2 as more social, but she can be really sensitive to what she perceives as slights or ill treatment, so she's not always easy to get along with.