You know, I'm not sure if this is done in Canada, but here in the US a common solution is for the wife to keep the house until the youngest child is 18 (sometimes with wife carrying the mortgage payments, sometimes splitting the house expenses) and then the house is sold when that child turns 18 and the profits are split at that time.
Ask your attorney about this. I know your H wouldn't like it because he doesn't get immediate cash, but if the alternative is moving the boys, he might relent.
Also - it's not your parents' job to take on risky mortgage debt for you. It's too bad that they promised you and reneneged, but it is probably a sound financial decision for them to make.
As for moving - would it be possible for you to rent for a while in your area until the kids finish school, and then buy something in a more remote area? Make the best financial decision for YOU long-term, but consider all the options.
