OP,
He left the family home.
He does not get to push his way back in.
That is not how it works.
This is a very nasty man who has clearly displayed his contempt for you and your children.
His belongings are with his mother.
In effect, he no longer lives with you.
Please do not hesitate to contact the police.
As he no longer lives with you, I think you should change the locks.
On the basis that having left the home and having clearly told your children, who are old enough to clearly repeat what was told to them, he no longer lives at your address.
Flagging the house at 101 will put your home on the police radar.
He doesn't get to leave, change his mind and bully you.
Remain very calm.
You need to see a solicitor asap, so that you can clearly state, he left the family home and is now demanding to return.
Stress that his belongings are no longer at your address.
Please reach out for support from family and friends.
He cannot bear that you aren't on your knees begging for his return.
This is all about his ego.
You are doing great.
Can someone change the locks?
Can you ask someone to buy and replace the barrels.
If he becomes even slightly aggressive, you have every right to protect yourself, your home and your children from his erratic behaviour.
