Can you file to get official possession and occupancy of the home? Many courts support such petitions, reasoning that it would likely reduce risk of conflict and DV incidents and hasten the process of unwinding the marriage.
Yeah, I think this is the way to go too.
Find a lawyer if you can. Put into your motion the reasons why you should not live together; the reasons why it makes more sense for him to leave than for you to leave; the schedule you think would be best for the kids - like most of the time with you but certain days with him; and the reasons why you think this is urgent and should not be delayed til the divorce is final.
Living with someone who you have decided to divorce is very stressful, and it's not good for anybody to live in such stress for long. The courts understand that and will probably help if your reasons are stated clearly.