When the owners are not married, the fact that one may be taking care of a child is irrelevant. When unmarried people, even ones who live together or even have a child together, own property, they (assuming they are 50-50 owners) have equal claims to it. If the can't between themselves work out what to do with the house, all a court could do, if one of them brought a lawsuit "for partition," is to order that the house be sold and the proceeds (if any) after paying off the mortgage and any liens and paying any costs of sale, be split between the owners--that's the only recourse under the law, to bring a lawsuit to force a sale. Otherwise, it's whatever the two owners can voluntarily work out.