See the thing here is you really have to flush this out- do you feel your child/children are put in danger by this lover man? Have they stated to you that they feel fear for their safety while he is around?
And for what its worth, it looks TERRIBLE that your ex is shacking up with the lover and exposing the kids to this- as it seems really unstable. And I dont blame you for being upset.
But if you dont think they are in danger, and you just plain don't like it- there's nothing you can really do about it unless this guy is like a criminal or something.
BUT- if the guy is like parenting in lieu of your ex, that isn't ok either because you should have the first right of refusal as a parent. I have a clause in my divorce decree that states if the child will be with someone aside from either parent, the other parent has the right of first refusal as it is always better for the child to be with a parent except in cases of abuse.
But also, be very careful about what accusations you make in court and be certain you have proof, because falsely accusing would make you look like a nutter butter which could hurt your custody proceedings.