Can a domestic partner take your home if you have a child together.The Mortgage is in my name.

Generally, a domestic partner will have no rights to the home that is solely in the other partner's name.  However, there are exceptions depending on the circumstances.  It could be possible for the custodial parent to have the exclusive use and possession of the other parent's non-marital home if the other parent has a second home.  In such a circumstance, child support would be lower to account for the custodial parent's use of the non-marital home.