There is no automatic legal right for a mother and the children to stay in the family home - it's preferred yes to provide stability but Her DH has no obligation to pay the mortgage or pay anything above his minimum CMS requirements. He also has the right to a home of equal value and status to enable the children to stay with him too and if that means the family home being sold then so be it
@ivfdreaming is, unfortunately, pretty much right.
The ideal scenario is for the children to be housed in a way which meets the expectations they have had thus far. In reality, though, there is rarely enough money available for one parent to keep the family home and the other parent to buy something that is appropriate for their needs. This will normally, sadly, mean that both parents have to buy something else.
The starting-point is 50/50, adjusted to accommodate individual circumstances. The needs of the children come first. If both parents have worked, the mother will not automatically be awarded a greater slice of the pie. If the mother hasn't worked, but would now be able to (though we all know that in practice, anyone who has been a SAHM for any length of time is stuffed in terms of employability), the same applies.
It's crap. And especially crap for the children.
OP, I know it is hideous, but you have done the right thing (for now, at any rate) not blaming your husband. I was the one who ended my marriage, because my husband was a vile abuser. We agreed to tell the DC it was by mutual consent. XH instead told them that I was leaving him, and it was all my fault. It has taken years for the children to forgive me - even though I have, gradually, told them why I had to do it. They are still emotionally stuck with "Mummy is splitting up our family because she doesn't love me". It's a terrible thing to do to children who are not old enough to understand the complexities of adult relationships and who are already going to be cast into unspeakable unhappiness.
for you, OP. It's a hard road, regardless of who instigates it.