I disagree - if the house is underwater still, I don't see what value there is to forcing a sale (and you still have to count the second mortgage, so it's still under water, correct?)
And I actually agree with the GAL - it is a very bad situation for the kids the way you are living, and it would be better for the kids if you two could split ASAP.
I know you have concerns about finances, and need to get things worked out in such a way that you can afford to move. But I also know that the rest of this stuff - criticizing his parenting style, bickering over how much kid contact you can have on each other's days etc. - is stuff you simply have to LET GO of. No, you won't be able to keep your kids from being around OW when you're divorced. Yes, OW might move into the house if he keeps it. Yes, he might do things differently as a parent than you would (all dads do - and btw, it really wasn't irresponsible of your H to leave your daughter in the bathroom to brush her hair. You can't watch kids every second of the day, and that was not an unusual situation - your D just did an unpredictably wacky thing.Not his fault. And no, bleach is not good for you, but it does kill mold, and if you cleaned the bottles thoroughly enough afterwards, probably no more chlorine exposure than one trip to a swimming pool.)
You keep telling H what he CAN'T do in this divorce settlement - maybe you would get somewhere if you presented him with a workable plan that gets you out of the house ASAP? Something like:
- x dollars in temporary support (have you filed for temporary support yet?) - a REASONABLE list of the 1/2 furniture you want - x dollars for deposits and last month's rent on an apartment - 3 month limit on refinancing versus putting the house on the market. (It doesn't take any longer than that to get through the process.)