I haven't read all the replies, only some. While I know child free weddings are common, heck I had one myself, I think an exception should he made to nieces and nephews, it doesn't have to extend to all guests' children.
For your SIL to just assume your friend with 3 children already will just look after them (???wtf???) is ridiculous!
Sorry I have no advice, but wanted to say I understand and agree with your feelings on the situation.