What is the ruling on a man remaining with his wife while concealing the fact that she was inseminated with sperm from someone other than him, after he has repented to Allah?

These children are not his. He must disown them and hand them over to the government or let them stay with their mother, on the condition that they are not attributed to him. The Hadith, "The child is for the [owner of the] bed," is not applicable in this case.