Your H is smoking something if he seriously thinks he can wrest full custody away from you. He's either trying to bluff his way into more concessions from you, or he thinks he can somehow prove you unfit -- not likely by any stretch.
I still think he's dangerous however, if for no other reason than he's willing to put such an expensive motion before a judge. With any luck, the judge will not only be unamused but ready to slap him down for silliness.