I went through a custody battle three years after my divorce. One thing you should keep in mind is that a child truly needs the balance of two parents, no matter which parent he or she lives with.
As long as the child is with you during the week most of the time and you are the primary caregiver, I feel that there will be no problems. If you feel that he is trying to take this child from you, remember, YOU DO NOT OWN THE CHILD!! NEITHER DOES HE!! The one who will suffer most in a custody battle is the child. Please keep this in mind as things unfold. I hope you and your ex are in communication. This can help to prevent any ugly battles in court.
For the first three years after our divorce, we had joint custody. I, however, was the primary caregiver (my son was with me about 70% of the time). When it came time for elementary school, his mother took me to court and sued for full custody. The judge threw it out of court so she appealed. She won the appeal maybe because she is the mother or because my business took so much of my time even though it did not interfere with my ability or efforts to give him proper care and there was nothing I could do. (I don't understand the appeals courts)
As long as you are giving proper care to your child and not abusing him or yourself, he will not be able to take custody. The fact that you are willing to grant him extra time with the child also is in your favor.
My son has always been in my life, even after that bitter court session. He has always looked to me for guidance and still from time to time does. He is now 32 and lives in Japan (as do I) but most of all, we are best friends.
If you're the POA then you can pay her bills but her bills are still her bills.