Even if we assume the government has a compelling interest to be involved (though a close reading of Troxel decision would seem to indicate otherwise), the govt. is still required to employ the least intrusive means. In this case, there are clearly less intrusive means, such as a rebuttable presumption of shared parenting. There may be even less intrusive means as well.
The govt's means of achieving its compelling interest is over inclusive, because it drags in many children of separated families who have not requested, and do not need or want, and would in any event fare no worse or even better, without the govt's "help." The means are not sufficiently narrowly tailored to the objective, the objective is vaguely defined, and the results are contrary to the objective.
Just a few more thoughts to play with, I assume you had considered most of them.
Good Lukc.