Is it permissible for a husband to prevent his wife from seeing, speaking with, or sleeping next to their children, as a punishment for her disobedience, knowing that she treats them well, or is that forbidden for him since custody is her right?

A husband does not have the right to prevent his wife from seeing her children, speaking with them, or having them sleep beside her. The wife's disobedience (nushooz) does not negate any of these rights. Nushooz negates some rights, such as financial support (nafaqah), and gives the husband the right to discipline her through specific means prescribed by Islamic law.