The husband is merely trying to protect his wife and child from further emotional abuse. It's understandable that he wants to shield his infant from a toxic environment, especially given the MIL's history of verbal attacks. He is not forbidding his wife from seeing her family, but rather setting a boundary to protect his child's well-being.
The husband's controlling behavior is isolating his wife from her family. While the MIL's behavior is questionable, the husband is punishing the grandparents by keeping the baby away. The husband is using the child as a pawn in a family power struggle, and he is being overly sensitive to his MIL's comments.
While the MIL's behavior is undoubtedly toxic and uncalled for, the husband's response is a bit of an overreaction. The wife is capable of making her own decisions about her family and her child. The husband needs to trust his wife to manage her relationship with her parents and focus on resolving the conflict directly with his MIL, rather than restricting access to the child. He should be more supportive of his wife's decision.