If you cannot agree on how best to provide a home for your children, and the case goes to court, the priority will always be the welfare of the children.
Where a family home is the main asset, you (as the primary carer) and the children would usually be allowed to remain in the house until the children have finished their education.
However, where finances simply do not allow for the cost of maintaining the family home, you may have to be realistic about moving into a smaller house. This could be a positive new start: for example, a smaller house will cost less to run.
This can be a contentious area, and it is one where you should seek legal advice before making any major decisions. Mediation should be considered early on if you need help resolving financial issues. You must attend a mediation session before making a formal court application.