Just as you have discovered 'venue' deals with one county vs another county. Your situation is governed by statues known as the Uniform Child Custody Jurisdiction Act or Enforcement Act (UCCJA / UCCJEA). Each state will have enacted it's own statues which may negate the intended uniformity (which gave rise to the federal statues known as Parental Kidnapping Prevention Act (PKPA). One main purpose of these acts is to protect the CHILD and left behind parent from involvment in multi-state litigation. Jurisdiction WILL, in most situations, be the childs Home state .. where the left behind parent resides. Attorneys love to make money fighting these jurisdictional issues. You must check out your state statues. The foundation UCCJA and the PKPA is documented in the articles section (bottom of page). Here is a key excerpt from the UCCJA :
Jurisdiction to make child custody determinations. 1. A court of this state which is competent to decide child custody matters has jurisdiction to make a child custody determination by initial or modification decree only when:
(a) this state (i) is the home state of the child at the time of commencement of the custody proceeding, or (ii) had been the child's home state within six months before commencement of such proceeding and the child is absent from this state because of his removal or retention by a person claiming his custody or for other reasons, and a parent or person acting as parent continues to live in this state; or
In short, from what you described, dad or mom needs to request modification in the home state or state of most recent action involving the child.
I'm not an attorney .. just btdt