a probationary rental period would be extremely disadvantageous for the tenant, for example if you move because of a job change and then get kicked out again two weeks later...
legally speaking, it is very difficult to enforce your rights, especially when children are involved, as there are various possibilities that such nomads exploit. getting money from nomads is almost hopeless.... if they at least clean up and paint, okay, you only lose the rent costs, but based on the points mentioned, I can't think of anything lawful.
I would then resort to vigilante justice, which is of course punishable and I do not want to encourage anyone to do it, but everything has an end – except the sausage, and this is not about that.
what landlords like to see are Hartz IV recipients including an assignment declaration, which means: your tenant goes to the office and fills out this declaration so that the warm rent is paid directly to you on the 1st of the month. this way, he simply does not have the money available and is a pretty safe bet for you as a landlord. a worker, on the other hand, if he suddenly becomes unemployed, just can't pay at first – and you all know yourselves that can happen to anyone! therefore, as a landlord, you should anyway build up reserves as quickly as possible – then a fair landlord who can also wait a month for a payment gains a lot of respect from the tenant! and a fair rental relationship based on both sides is priceless!!!!!!!