Extracurricular activities can be fairly minimal, or can be thousands of dollars per year, per child - especially if the word "travel" is involved. Because the costs are usually on the low end for younger children, parents often don't consider the costs at the time of separation, but only when they've reached their full, teenage levels.
Does a parent receiving child support have to account for how the money is spent?
Appeals in Family Law
How are child support orders enforced?
Where will my case be?
There are two issues surrounding where a case will be filed - jurisdiction and venue. There is a course in law school dedicated almost entirely to these issues (civil procedure), so unfortunately I can't give a comprehensive answer to the question that suits every situation. The general rule is that cases must be filed in the state and county where the person you're filing against lives, but divorce and family law have more exceptions to that rule than probably any other area of law.