How bad is your DP's ex, really? You've made her sound so bad that its amazing she got custody of child. Or did your DP not go for custody? Odd if he didn't, since he cares about his DD so much and the mother is violent and involved with drugs...
Whats he going to do if he meets her man? Does he have superpower skills that will tell him if this man is good, or not? Is he going to quiz him about their relationship/whats he going to do if he's told to fuck off and mind his own business?
If the child seems happy and well cared for isn't that the most important thing? You haven't intimated that child is unhappy or neglected
I don't buy this story at all tbh. & I think your DP is far more concerned about his ex than his child but like many women you buy the story that the ex is a crazy bitch, unstable, has unsuitable partners. Funny how so man living saints men say this and YET they chose to create a child with such an unsuitable woman Then when they're apart, spend their time monitoring her life
In your shoes I truly wouldnt be happy with a man so focused on what his ex is and isn't doing - it doesn't bode well for your relationship. Again - if his child is happy and well cared for, not showing signs of instability and unhappiness, then that is all that should matter.
I just know too many women who are labelled as crazy by men, when there's no history of them being unstable at all. & the new partners joining in with all the talk. There's no need for it. You don't have to be your mans' Knightress in shining armour he can fight his own battles, although if he is yapping about his ex 24/7 then it will get on your nerves
If he's that worried he can voice his concerns to the correct services can't he. Somehow, I doubt that he will
Good luck tho OP, you've got this until his DD is at least 18. Thats a long haul.