These kinds of cases (and other kinds of court cases too, court is expensive) tend to run 5-10k per court date in legal expenses. And the most likely outcome of any given court date is . . . another court date . . . without a change in the status quo. It typically takes 3-6 court dates to get an order changing the status quo, and maintaining the status quo is much cheaper and less demanding than changing the status quo. Do the math here on how much $$,$$$ it is likely to take to change the status quo.
A Louisiana court (most likely) has granted joint custody. Most likely, a Louisiana court will view a request to move out of state over the father's objections as an attempt to reduce the father's influence and input into the childrens' lives, especially if the justification isn't much more than a lifestyle preference by the mother and step father.
Even if you have justifications that would be viewed by the court as more than lifestyle preferences (and can make a case that the move is in the best interests of the children) the justifications will be weighed against the reduced opportunity for paternal input and affection, and this is where changing the status quo will likely require multiple visits to court and five or six figures of legal investment, not to mention months or years of time and stress for the marriage and the children.
If you must move, negotiate an arrangement with the father. In the long run, it will likely be better for your step-children and for your marriage than slugging it out in court. Make an offer where the children are the clear winners in a move: offer to send the children to a nice private school, or offer to meet some long held wish of each child: a horse, or a musical instrument with private lessons, or gymnastics lessons, or ..." Whatever it is that would really bless each child. Children give up a lot in an interstate move: existing friendships, the stress of a new school and new neighborhood, new sports teams and clubs, etc. Convince the father that the children will be the big winners, and pray that God will open his eyes and heart.
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