move with kids

Can I just leave my abusive ex and move to the other side of the country with the kids?

A court order is required to prevent a parent from moving out of the
state. If the parent who has physical custody wants to move, and the
other parent protests, the courts in most states have the authority to
decide, on behalf of the children, whether the custodial parent may move.

The courts typically consider the following factors:

Whether the move will improve the child's school or community.
Whether the parent's motive was to harm the non-custodial parent.
Whether the non-custodial parent's motive in resisting the move is to
harm the custodial parent.
Whether the non-custodial parent will still be able to have ongoing and
significant contact with the child.
The nature of the non-custodial parent's contact with the child so far.
In cases that denied the move, a consistent theme is that the other
parent has spent many hours each week with the child, consistently
showed up for all his or her visitations, and established a close,
supportive, and loving relationship with the child.
The effect, either way, on the child's contact with grandparents and
other people who are important influences in his or her life, as well as
contact with the child's native culture.