He can ask the court to prevent you moving, with or without PR. I doubt he would succeed. I assume you are in England/Wales, and your move will not take you out of England/Wales.
PR only really comes into it when a move means changing schools.
In your circumstances, I would just get on with moving, so that you have famiky support (That's shy you're moving, iirc?)
If he applies for child arrangements, or PR, it'll be 2 -3 months before first hearing. CAFCASS will have police and SS information at that hearing, and at that hearing, the Court is reasonably unlikely to order contact unless you agree. S7 report should be ordered. Also hair tests for relevant drugs (not cheap, and someone will have to pay.) Specify what "drugs" you think he was on.
www.lextox.co.uk
You need to go to court with a clear idea what tests you want, and how much they will cost.
Long term, if he persists, the starting point will be contact centre contact, unless family can supervise. Personally I think family supervision is the most stupid idea on the planet (excepting only having the resident parent supervise) because a) conflict and b) evidential problems if things go wrong : the Court is just left with witnesses all saying each other is lying, and no impartial evidence. But that's never stopped a professional judge, so it sure won't stop a bunch of magistrates ordering it.
After that, it really depends how it goes.