I have three suggestions,
(1) the neighbour should take up the lease of the house and pay the rent for the duration and pay her moving expenses and then your daughter can move to a home where the dog is not a "bone of contention". This is a win win situation. The neighbour will then be able to live securely (for the duration of the lease) without his son being "traumatized".

As an aside, have you ever considered where the son has learned this behavior = sounds to me like a convenient scapegoat for the father. "I don't like dogs, I will teach my mentally challenged son not to break into other people's homes and abuse the animal and the people, and therefore my son will be given leniency because of his incapacity". A sorry father figure and an even sorrier police response.

Or, your daughter is renting? Get her Qatari landlord to speak to the neighbour. The landlord has a vested interest in getting and retaining good tenants, if the neighbour is abusing the landlord's tenant, then the landlord should be following up as the police seem to be unwilling to do so (despite the Qatari laws).

Thirdly, the next time the fellow breaks in, call the police and have him arrested. He is breaking and entering no matter his "rationale" and your daughter and children are vulnerable, if the officers on the scene won't do anything demand to speak to the next highest officer, asking what would THEY do if it was their daughter, sister, etc. in the same situation.

This "kid" sounds physically dangerous - If I did what he has done, I'd be in jail no matter my explanation.
Signature line > "You can't fix stupid"