The first question I would ask is why you intend to file separately for 2013? There are many disadvantages to filing separately. Tax rates are higher. Most credits are not available. It is almost always better to file married filing jointly.
When TurboTax asks about the child's other parent, it is most likely referring to the natural parent in the situation where the natural parents of the child are separated, divorced or never lived together. In such cases, divorce decrees or other legal agreements can allow the non-custodial parent (who the child did not live with more than half the year) to claim the dependency exemption for the child. In some cases the custodial parent (who the child lived with more than half the year) must give the non-custodial parent a signed form 8332 or similar statement allowing him or her to claim the exemption. So the dependency exemption must be determined.
The custodial parent who the child lived with more than half the year can get certain tax benefits for the child who they claim as a qualifying child regardless of whether they claim the dependency exemption or not. Only one of the persons who the child lived with can claim the qualifying child benefits.
