Yes, YABU.
I hope you are reading and taking note of the posters saying that your new boyf is lying to you. He is clearly dangerous and for once, the police are actually doing their job properly, inviting you to make the application you need to to find out the truth about your boyf's past.
Also, tbh even if he weren't lying (which he undoubtedly is) where the fuck are your priorities right now? If the police hate your boyf enough to harass him (if their behaviour could be defined as harassment) then why do you want him in the house?
This is not a man you've loved for years, the father of your children, with whom you've been through thick and thin, whom the nasty Old Bill have suddenly started harassing for no good reason.
This is a Johnny Come Lately bloke of whom you know absolutely nothing, who has come to the attention of the police to the extent that in his eyes, they're prepared to harass him.
Now, police resources are thin. They don't have time to harass many people. If they've decided this guy is worth harassing, even if he is Gandhi and utterly blameless, why are you bothering to have him and his baggage around? You have much bigger fish to fry. Your DD needs all your energy and help and support, you don't have the luxury of being able to concentrate on helping your poor innocent boyfriend withstand police harassment. Your priority should be your daughter, Gandhi can stand on his own two feet.
Except he's not Gandhi is he. He's obviously a violent, dangerous abuser and you're burying your head in the sand about that because you want a boyf. Let him go. Concentrate on your dd, she needs you.