Even if I say no, I know he will just turn up - AIBU to refuse him entry if he does?
FFS - YANBU!
First up, its your gaff, & you can tell anyone the hell you like to piss off out of it.
Secondly, DN is a grown man who ought to know better. So he knows he is taking the piss - he's got ears. He's a manipulative fucker who broke his young cousin's kit & needs to take responsibility for that. No privileges until he does, I reckon.
My mum doesn’t seem to see a problem and won’t enforce any sort of boundaries, but will complain about him afterwards.
DM needs to get on-board with you OP, & pronto.
Suggest you start that process by telling her you have decided that DN is on a temporary ban & you expect her to abide by it. Your rules, your house.
Then make sure she is listening when you ring DN & read him the riot act. Along the lines of "you were asked not to invade DS's room, did so anyway, & broke his camera. You are taking the piss, & are not welcome until you apologised to DS & replaced his camera."
Leave it at that - hang up on him if he blusters or pushes back.
When he ignores that, as you suspect he will, & turns up anyway - greet him at the door with exactly the same words. Anything other than an instant apology - shut the door in his face.
With luck & a following wind, DM will feel empowered by your assertiveness & hold the line. Because his next trick will probably be to sneak round & whinge to DM when he knows you are out ...
Good luck OP. Take your power back - it's your gaff, & you have no need to allow a 22 year bellend to push your boundaries in it.