Just saying that I know exactly where you're coming from. Same thing happened to me, my husband just 'changed his mind' (I suspect he's seeing another woman). This past month he's tried agression, violence, intimidation, solicitors threats to get me to leave, and I'm still here!
I think my ex is trying to sell the house over my head, and embezzle me of money. I took legal advice, they said I should not leave 'for his convenience'! It's hard to stay put, but if I left he could claim 'abandonment'.
If I was you, I'd walk straight back in that door. I'd suggest to her that she conducts her sex-life away from the family home, and away from your daughters.
Keep a 'conduct diary', and keep your cool! (Impossible I know!)
If there is to be a divorce, the courts will base a settlement on 'need'. And usually the carer of children will stay in the
matrimonial home. You may keep a share of the equity in it, but she'll probably stay until they are at least eighteen.
Lots of advice here on where you stand, but I'm just suggesting that you don't let her 'bully' you out of your place, so she can conduct her fantasy life there.
I know you're hurting, it's called 'Divorce Hell'. You loved this woman, and to know she's in bed with another lover must hurt like mad.
A month ago I was missing the love I'd shared with my loving husband, since then I've stayed here, and seen this man I once loved become an ugly, manipulative, controlling MONSTER! When I finally have to go, it'll be this disgusting human being, and his hatred of me that I won't miss!
I'm missing the love less and less as the days go by.
It will take time for you to get through all the legal channels, you're right, it's a very slow process.