Can my son get primary custody of his daughter.

No, custody does not automatically go to the mother, but it sounds as though Tennessee may have custody jurisdiction over his daughter, and if so a Tennessee family law attorney is the best source of information regarding his custody case. If the marriage is not to be reconciled, he should get on with it and file while he has the child with him. Jurisdiction over the child will be in the state where she last resided for six consecutive months. In Texas and probably in Tennessee he must convince a Judge or a jury that it is in the child's best interests for him to determine her primary residence. He should get family law counsel in Tennessee. Whoever files first that location will have jurisdiction over the divorce and the child.

Your son needs to talk to an attorney in Tennessee ASAP. No the children do not automatically go to either parent.

As the others have stated above, your son needs to contact a lawyer in his state as soon as possible. Custody determinations are not automatically made based on the sex of the child and the parent, i.e. just because the child is a girl does not mean that the mother will automatically be awarded custody. The court will look at what is in the child's best interest in determining the custody arrangement.