The deep seated assumption that men are hard done by never ceases to amaze me:
Although I sympathise with you, I equally sympathise with your husband.
Why? he's purposefully making it difficult for the OP - refusing to compromise on sleeping or working arrangements, doing F* all in the home to help?
You have no more right to the house than he does, and his solicitor will have strongly advised him not to move out until you have something in writing about child arrangements and financial split.
Individually, sure, perhaps not. But as the main carer, of course she does because this is ALSO the children's home. I see OP says he wants 50% custody. Hahahaha. As it's pretty clear she is doing the vast bulk of the caring, I think we can safely assume he isn't interested in 50% care at all and that therefore OP and the children should absolutely get priority for the house.
It is a shitty situation for all and you being aggressive to him for working from home is not helping. And now, with his retaliation, you have both reached a new level of unpleasantness.
WTAF? He is working from home in the shared communal space, refusing to use the bedroom that is now for his SOLE use, while simultaneously refusing to go into the office. Even though the office has specifically said they want him in 2 days a week.
My best advice is to move along with the divorce as fast as possible and be polite (although not a doormat) in the interval. Negotiate a fair split of chores and house access, as you would with a housemate.
The OP has said nothing that suggests her ex is even vaguely interested in doing any chores, never mind a "fair split" .
If you keep it amicable, it will get done quicker and minimise the harm to your children.
Obviously it's all on her to be amicable.