Show your husband this thread. If he doesn't have a solution to this problem, you two will find one here.

Please excuse this giant wall of text, I feel like some things need to be addressed, and I have a tendency to rant.

DH: Stop being a spineless ass. Listen to your wife, take her feelings seriously. If you don't set boundaries now, your mother will think she can stomp all over you. She'll manipulate you to hurt your wife, as have many other jnmils.

Snatching a baby away from its parents is NOT ok. We here in my family call that baby snatching, regardless of intent, and regardless of who is doing it. If MiL snatches the baby up, you snatch that baby right back from her and whisper-yell/growl/snarl/(insert terrifying mama bear or papa bear voice description), "No, MY baby." ("wife's/DH's name's baby" and "our baby" will also suffice, though the latter should be said while leaning close to your spouse for the added effect of unity).

Your immediate family is you, your wife and your child. Their needs come first. You and your wife are a united front. Your married, for fuck's sake. You love each other, so communicate and take one another's feelings seriously. And if you don't have a solution to the problem: DH, meet jnmil. We're here to give you and your wife advice and support regarding your mother's baby rabies. Pull up a seat and grab your favorite snack, you're in for a wild ride.

Now let's clean that wound before it festers and hurts your relationship, because I can guarantee you that your mom isn't simply joking around; she's gonna cause some issues. She's going to hurt your wife's feelings in ways you probably couldn't imagine before (like the baby thing, and you dismissing it as as joke) and if you let her do it without consequences, that's gonna leave a mark. Please don't be the spineless husband that allows his mother to push his wife around.

Some miscellaneous MILimination tactics: If she asks "where's my baby," DH answers, "right here, mom!" If MiL corrects him and refers to your son, DH wails, "am I not good enough for you anymore?!"

Pull the Alzheimers card if you have to. "No, mom. This is OP's baby. I'M your son." "Your memory has been worrying lately. This is the third time this week you've mistaken our son for yours. I'm just really concerned for your health, mom."

Give her snark. Give her sass. Let her know that OP and DH are united, and good luck.