This question is covered pretty well in the more general, but for convenience, I will summarize my answer here:
Whenever the child is uncomfortable/awkward with the arrangement, and/or endangered by others.
If a 12 year old girl doesn't mind changing clothes in a locker room full of guys, that's absolutely fine, though it certainly indicates a potentially underdeveloped desire for independence if it holds much longer than that.
Technically, there really isn't anything the law can do about it until the child is 18 in most US states. The pool staff, however, might start enforcing their own rules on the matter well before then, especially if the other men in the locker room start complaining directly (my gym seem to draw the line basically at puberty, but as far as I know these aren't guidelines that appear in any official manual).