My question involves a child custody case from the State of: Oregon

My ex is threatening to move to California before my child is born -- thinking that if my child is born in another state, then she will not be restricted to stay in the state of Oregon (current residence of me and my ex).

She also told me that even if she doesn't move there permanently, but instead visits her sister in California and waits until she gives birth --resulting in the child having a California birth certificate as opposed to Oregon--then she will have the freedom to leave the State of Oregon whenever she wants.

Is any of this true? Do I have any legal options?