I'm confused on the housing issue. You say you have to come up with 120k to buy her out of the house. What about her? Can she afford to buy you out? If so, wouldn't that be 120k in your pocket, that you could use to get housing? If not, then it seems neither one of you can afford to buy the other out, and the house will be sold as part of the divorce settlement, and you'll split the proceeds, with both of you then needing housing, and you use the courts at that point to make sure it's in the same city or town.
I'm positive I've never heard of anyone losing custody of their children because they can't buy their spouse out of their home. With kids, it isn't pay to play. I see that you have a solicitor/attorney -- is this really what you're being told? Is it possible you're misunderstanding the advice you're being given?
Four months is not much time, by the way. Certainly not in terms of a wayward "seeing the light" and coming back to your relationship. The bigger question is why, four months on, you are you still pursuing her and giving her so much headspace?
Me: 46 W: 44 Married: 17 Together 21 D13; S10 BD: 03.03.15 (Not attracted to you) Almost 2 years trying, alone, to save marriage Status now: Divorced (effective 06.13.17)