Wow, sorry this happened to you. I am fairly new to being a landlord so I am no expert but I did just went through something similar but not as severe.
1. Late rent is not something to "get used to" One late payment fine, it may happen. But the second time I would give a warning or a 3 day notice (or whatever the law is in your area)
2. If both people signed the lease they are both legally and financially responsible for its terms. Just because he got another job doesn't mean he gets a get of my lease free card.
Second, if you do not have a sublease clause in your lease, as well as a visitors vs. occupants clause you should. You have a right to screen and approve anyone who will be living in your property as well as collect extra rent and security deposit for each additional occupant if you wish. I personally would never knowingly allow anyone to live in my property without them being on the lease (therefore also being a responsible party that I can go after in court) and putting them through the application and approval process,
In this case I would have held the brother liable (assuming he's on the lease) until the new ones could be approved (which they probably couldn't - that's why they are moving in instead of getting their own place). If they did get approved I would at the very least draw up a new lease including their names etc. But more than likely given the original tenants history with late rent I don't think I would have cut them any deal and just ask them to leave or evicted them on late rent.
Bottom line - If you KNOW someone new is moving in get them on the lease BEFORE they move in even a toothbrush!
3. I reiterate my point from #1 - do not let late rent become "something you get used to"
No, depending on what your lease says, it is not legal for them to move in without your approval. But your lease is the governing document here - if you have no clauses, it would make it harder to prove.
That being said, even if it is against your lease (therefore illegal) you can't just go over and kick them out. Or for that matter the police will not do it either. They will tell you it is a legal matter. You have to take it to court and evict the actual tenant for breaching the lease.
4. Unfortunately it sounds like you were dealing with "professional tenants" here. They knew how long they could stay rent free, and they pegged you as being "easy" so they got even more time rent free due to your delay in filing for non payment.
As for the utilities - it is my understanding (at least in my area) that you are not allowed to shut off the utilities - they call it forcible eviction here. I always thought this was a crock IF the lease agreement states they are required to pay all the utilities and put them in their name. In my mind, if this is the case, I am not forcibly evicting - I am just enforcing my lease terms by not keeping the utilities on in my name. This is fortunately a situation I have not had to deal with but something I will be checking into.Maybe someone else knows more on this.
Just remember this is a business and you have to run it like a business. Tenants are not your friends, they are someone you have a business arrangement with. Have a good lease and stick to its terms. Sometimes you can show a little leniency but not too often or you will get burned.
Good luck to you - I hope your next experience is a better one.