How would you have handled this situation? SIL disciplining your kids while you're there?

I would have dealt with it right from the start when she was telling my child to get down here now. I would have simply said "once she goes down the slide she'll come over, leave her be." If for some reason it got to the point it did where she was pulling on here I would have told her "get your hands off my child now!" I wouldn't have put up with that. I think its a little strange to address it after the fact. From this point on I would just step in before she gets the chance to go after your kids. If she starts to say something to your kids I would kindly ask her to mind her own business and worry about her own children, you'll handle yours.