Legal Question in Family Law in Pennsylvania

You need to direct your question to a Texas family law attorney. Since you just moved to PA, TX has primary jurisdiction of the children. If nothing is done, TX will lose jurisdiction in another 4 months and any custody proceedings would have to be brought in PA.

Absent any custody orders, then both parents have equal rights to the care, custody and control of their children. If you are going to take them back to TX, I would do it in the next 4 months and as reasonably soon as you get there I would file a custody petition there so as to cut off any efforts by the mother to try and get this in PA.

As to whether you would have rights or not, I cannot say since you are not married to the mother. Being on the birth certificate may or not be enough. Some southern states require that the father also legitimate the child before the father can bring any custody action. I don't know how TX views this and that is why you need to talk to a family law attorney in TX. To my knowledge, PA does not have such a rule.