That depends on state law where the child currently resides and whether or not she intends to take the child with her.
Laws vary widely from state to state as do circumstances where such a move may be approved or denied, if court approval is required in the absence of consent from the other parent. In most cases, joint custody confers joint rights including the joint decision to approve or nix a move depending on the circumstances.
You would need to provide more information for an accurate answers.
When married you have equal rights to the child.
Does she want custody or access?
File a modification motion. see links
you can sign the custody over to her or she could go to a judge and try to prove you unfit to take care of them and prove her having custody in their best interest
No, he can't. It can, and if mother objects strongly enough, it probably will be considered kidnapping.
Yes, but I teach fathers how to change that.
the father gets the custody of the child if the mother dies
File for change of residential custody. see links
It can be but there would have to be a pretty strong case for it being more benficial for the child than the mother having sole custody.
wife
Yes, only Arizona is different.
If a child's mother has sole custody then the courts have decided this and there is a reason for it. Generally, if the mother is a good mother (fit mother) then the children will be looked after by her with the father having partial custody to see his children. If the father is unfit, then the mother would have full custody. If you are the child asking the question and are upset because your mother has house rules and you don't always agree with them then this is not a good reason to want to live with your father. Your mother gives you these responsibilities so you will learn good characteristics that will make your life a whole lot simpler. You may not see that now, but will in the future. If this is the father asking the question and you have partial custody the courts have deemed it this way for a reason. If the mother is unfit and the father wants to take full custody then you should retain a lawyer asking for full custody.