Often the mortgage lenders will not accept just one of the couple having the house as it is not financially viable. The wife may have to go back to work, but there will be child care costs. The husband wants his share of equity out of the house. he has to buy or rent elsewhere. Practical financial planning is needed. Perhaps selling up will be the only option and then using savings or cashing in policies.
The spouse who is looking after the children can try to seek a capital split more favourable than 50-50 to cover the cost of housing children but this is not in your case.