I don't have time to read the others, so I am sorry if I repeat.
I can understand your frustration if it seems like this is a pattern of not being consulted or considered, but I think in this particular situation, it was handled correctly.
Most families that have successful in law relationships have a policy of talking to the person who's family it is. Basically the rule that everyone handles its own family members. So if something needs to be dealt with in your husband's family, he handles it. And if you guys have an issue with your family, you handle it. That always seems to work out the best, and on almost every In Law question on this board, you will see that advice being given.
You might think, so why didn't he ask me and get back to them? But if he had done that, what is he going to say when he calls them back? "No Mom, she said she wouldn't do it." That puts you on the spot.
I think your husband did great in this situation, and maybe that is what has always been going on (on your husband's part). He wasn't letting you get taken advantage of. Because how are you supposed to say you don't want to babysit your sister in law's kid without looking like you are selfish, or inconsiderate, or whatever else they might think of you for saying no.
I think you should not feel bad about this situation at all and be grateful that your husband is willing to defend you to his family, unlike so many other ones I read about on here. Hope that helps you feel better!