I’m sorry you’re going through this.
A similar thing happened with my sister and her husband but it was rented accommodation, so I don’t have any advice.
Although it was my sister who created the argument and was the one in the wrong, the police took my sisters side.
So I would be very careful about going to the house or contacting her too much, else you’ll just be seen as the bad person even more so.
Are you in contact with her?
If not I would write her a letter and tell her that as she’s kicked you out of your home then you will not be paying the mortgage and you’ll be selling the house so you have somewhere to live.
It is then up to her whether she wants to buy your half of the house off you or sell up and split it.
In the letter I would ask to see your kids but if she says no then you might have to wait until you sell the home and get money.
Which is completely unfair but I doubt you’ll be eligible for legal aid.
This is not going to get better overnight.