I think you're cutting your nose off to spite your face, communicating with them on the issues you've listed and then making a decision either way would be the more professional way of handling it.
As for entering the property, no matter how much notice you give legally you still are not allowed to 'let yourself in' unless you have express permission from tenant, and that's regardless of what any tenancy agreement says.
Have you had the window locks checked by an independent party, e.g., not the person who originally fitted them? It seems a bit off to me that a young child is repeatedly breaking them. I'd be getting them checked to see if they're of a good standard, not defective, etc.
Was the tenancy a year long or six months? I don't know the exact rules but I remember reading that for a yearly tenancy you must give six months notice that the rent will be increasing.
Also their deposit should be in a deposit protection scheme, shouldn't it?
This is why, back when DH and I were renting privately, we made it a rule not to rent from people playing at being landlord and only went through agencies.