I don't know what state this is in but I can tell you what the law is generally.
You are actually a tenant in their place without a lease. That makes you a month-to-month tenant if they want you to pay monthly. Without a lease, they can change the terms of it if they give you advance notice, but they can't put you out on the street. They would actually have to go through the eviction process to get you out of the home. This sounds extremely disturbing -- do they work? Why would they suddenly need $500 a month if you are doing everything for the kids? Do they work during the week and have they suddenly developed spending habits that are out of control?
You don't have to answer those questions, and they don't have to tell you either. You might want to ask yourself if you've seen any change in them.
In any event, I am so sorry you are going through this. You are only 3 yrs older than I am and it's not something that we need at this phase of our lives, so I truly sympathize, and I can relate to a difficult child or in-law.
That being said, they must actually evict you. They have to serve you with notice to quit or a notice -- the time depends on what state you are in -- it could be 3 days, 7 days or 14 days. That does NOT mean you have to leave. They will think you have to leave but you don't. They can't throw you out. If they do, you can sue them and collect money damages for illegal eviction.
It is as if they are your landlords. To buy time, you can stay there even if you are given a notice to quit, and then what they must do is they must serve you AGAIN with either a summons and complaint or a summons and petition for eviction. Then you will be given a court date and the case will go into court. If you want to slow it down, ask for a jury trial. If you need a landlord-tenant attorney, let me know where you are (nearest big city) and I can find lawyers for you.
It is not legal to throw you out, but it is legal to change the terms of a month-to-month agreement. As long as you don't have a lease, there is nothing preventing them from changing those terms. I would suggest you either work out arrangements with the parents or find another place to live. It seems like they're taking advantage of you, a lot, and that's not fair. I don't blame you for being upset.
Does this answer your question? Let me know if you want me to find lawyers for you, just in case.