Hi,
I think it’s absolutely essential that you contact police asap and let them know he’s moved in opposite you and that he made the malicious child safety report. The recency of these two actions alone are very concerning, given he has a history of harming the children too. Cameras, change of locks (including the rear gate), drawing your curtains before switching on internal lights (he’ll be able to see through net curtains at night time if the lights are on inside your house and the curtains are open still).
Also, warn the school he’s moved in opposite you and that you have concerns for the children. Is there a court order etc banning him from picking them up from school without your consent? Make sure they’ve got a photo of him on their records and ask them to contact you immediately if he tries to pick them up from school.
Vary the routes and routine (where you grocery shop etc) you usually follow. If you drive a car and discover he’s tailing you, drive to the nearest police station, park up, don’t get out, and keep your hand on the horn and phone 999.
It would be a one in a gazillion chance that it ‘just so happens’ that of all the rentals or government lets, he ‘ends up’ directly opposite where you live. Has this been a typical pattern of behaviour by him towards you? How else might he have been monitoring you? Does he know where you work (if you do)?
Also, unless your post gets pushed through your letterbox fully each time, I’d consider having a mail redirection to a trusted friend or relative’s house (one he doesn’t go to), just in case he tries to read your mail before you can get to it: Especially important re: court documents/financial info etc.
Supervised visits within a contact centre (only) sound like a good plan. Where do your children play? Keep an eye out for him around them if they’re out in the street playing/walking home from school etc. Just in case he tries to convince them or snatch them into his home.
Sorry you’re going through this.