Regarding the house, does splitting it 50/50 put you in any sort of financial bind? It sounds like you've got "leftover" inheritance money even after buying the house.
To me, if you feel like she was an equal partner in the M, financially, at least, then to me it seems fair that you split the house 50/50. Not necessarily for her, but for your kids. You want them to have a good quality of life when living with their mom. Splitting the sale of the house will go a ways toward making that happen. That's gotta make you feel good. I hear you on the OM thing. The idea of supporting, even indirectly, that guy has to gnaw at you. I can't remember what the stat is, but the vast majority of A "relationships" end. He ain't likely to be around for the long haul.
Plus, your long-term goal is still to reconcile, right? Is going back on the mediation going to help that goal?
BD
My latest
Me: 36 W: 35 2 D: 9 and 5 T: 16 years M: 12 10/4/06: Bomb 10/5/06: Ended A 4/22/07: ILYBNILWY