A. No need to force your child to hang out with someone she doesn't care to. Maybe the kid is a little demon to your daughter when no one's watching, or she just doesn't like the girl's ponytails. Whatever the case, your daughter has her own reason for not wanting a playdate, and she has the right to it.
My 7-year-old's been teaching me this for years. She's turned down more than her fair share of playdates for the chance to color with her sister, explore the back-yard with her cousin, or sit and be still. I used to worry that she was turning into a loner, but lo and behold, what I thought was standoffish behavior was really just discriminating taste. Mari knows what and whom she likes and dislikes, and plans her schedule accordingly. If she wants to play with someone, she'll say so.
If she doesn't, she'll say that, too. It's not a big deal. So, if you get another invitation your child doesn't care to indulge, tell the other mom you can't make it. Eventually, she'll get the picture and stop asking.