Q: When can the male cat go back in the room with the mother and kittens?
A: After she’s spayed. Or after he’s neutered. (Preferably both). Otherwise, he can’t (or shouldn’t). Female cats can come into heat even while they’re nursing kittens and can become pregnant again. (I’m assuming you’re trying to avoid this. I hope so.) The mother can be spayed any time, but it’s best to do it after she has stopped producing milk and the mammary glands have shrunk back to near-normal size. This should happen a few weeks after the kittens are separated from the mother. This entire process can take a few weeks. The male, however, can be quickly neutered at any time, and can go back into the room with the mother and kittens soon afterward