My paternal grandfather always used to smell, and he used to deny the fact that he was smelling. He would never listen to my mom about bathing, or just using some sort of air freshener, but when my dad told him the same thing, he finally accepted it. Sometimes, old folks are unable to smell their own smells, having got used to it.
What you can do about it is that first ask your mother in law to put on some kind of perfume. If she asks why, or says she doesn't want it, just let her know (politely) that she smells, and you don't like it. If she denies the fact that she's smelling, tell your husband to try, and if you still have no success, maybe take her to a doctor whom she's familiar with, and will tell her that she's smelling.
If you can get her to accept the fact that she smells, telling her to wash up, or even helping her out to do it as you wish, might work out better. And, your child won't be troubled by the musty smell anymore.
But be aware that everything needs to be done in a way that your mother in law shouldn't feel insecure at any point. If she starts getting angry, or emotional, just calm her down.
(Although your husband would probably be best for this, if your mother in law is very fond of you/close to you, it's perfectly fine even if you do it.)