Anybody can file what ever they like with out basis at any time. You can go down and say...someone hit you (even if they did not) & file a warrant..When you get to court..is when evidence becomes a factor and the Judge gets to decide and or dole out consequences as the law allows.
He can make you jump through hoops for a bit..but the judge is not likely an idiot and will see through this and tire of it eventually. It is unfortunately part of the dance. Don't let it get to you..do what is best for your children and hope he moves on to his next prey soon..(as narcs do) and that he moves out of your and the kids lives.