Re: SIL dilikes my child. Cousins can't play.
People say and do such ugly ugly things! SIL sounds like a deeply unhappy person, and for whatever reason (perhaps some of what the PP said) she is taking it out on you and yours. I think all you can do is keep your distance. Do what you can to help Sophie understand that it is not *her* fault, but A* just can't come over right now, you hope she'll be able to some day, and get her involved with other kids, other friends. If you can find compassion for your SIL, stay open to reconciliation, but not at the price of letting her abuse you or be nasty to or about Sophie.
One thing... kids are very resilient about relationships in ways that adults are often not. My DD1 used to have all kinds of drama at Day care - who wants to play with whom, who is "friends" or "not friends" with whom today. DD1 would also get very angry sometimes and say things to her friends (I'll never be your friend again, etc etc). Sometimes I had to put her in her room and close the door and she would still be yelling. Later she'd feel sad, but her first response was always anger. I think some people are just like that and as she has gotten older she *still* responds that way but has learned to control it much better. But at 4... well I used to get upset and worry about it (both in terms of her being hurt and also feeling AWful about some of the things she would SAY). But then I also realized that a little while later they were all fine and I was the only one still upset.
Point is, this seems to be your SIL's problem first and foremost and saddest of all for her as she is the one that loses the most. It is sad that Sophie doesn't get to see A* but she is and will suffer from it less than you, even if she does ask about her.
Hang in there and don't take it personally. No matter what SIL says, this is clearly not about you or Sophie. It's all her...