As I posted to someone else last week, my philosophy is that each person deal with their own family. Your husband isn't supporting you if he can't speak to his mom and keep the boundaries. If he's worried about it because he's never done that before, brainstorm with him on what he could say that might work with her and feel okay to him. course, he might just have to man up to it, but there is no time like now. Perhaps he could say something like:
Mom, we need to talk. I love that you love our child. She is certainly my pride and joy. My wife, of course, is also my big love and sometimes I feel that you say things that are kind of out of line for a mother in law to say. You need to think about that a bit more because you don't want us to stay away more so that you don't cause upsets with your words.
(If she wants examples, think of some he's ready to say, like:) For example, you call ____ your baby. Now, you know she is our baby and your grandbaby. You probably are just in the habit of saying "My baby," but it is one of those things that just doesn't sound right to me.
You also sound like you disapprove of my wife's family by things you say. You may not mean that, but it is important, either way, not to indicate your discomfort of her family spending time or babysitting our child. They are good people that care for the baby. I know you are working and dad needs your help especially now because he might lose his job. I would feel awful if your security were jeopardized by that. Little _____ will be around a long time for you to enjoy.
It is so important to me that you, my wife, and my baby have a good relationship. But it's not going to work out well if you continue to say things or give looks that don't approve. Can you change that for me? It is so important that you do.
After that talk, if she gets to you, you could just give her a paused look (not a face) and then say, "..uh, I think I should go take care of ________ now. We'll see you later. Gotta run." (She will be stunned and speechless but she will get the point.) If you're at your house, you might have to make up an errand that you must go take care of with your child.
The goal is to make her be civil adn thoughtful or at least intimidated by getting out of line sothat you guys can continue a nice family relationship with her having boundaries. Only your husband can do that effectively. She will forgive him most things -- but not you, the daughter-in-law, as easily. And you don't even want your daughter growing up too timid to speak to grandma when she needs her boundaries or not having a grandma to talk to from your husband's side. Give her a good example of how to handle, and not just cut off, family.