This is a 2 part answer, pay attention to the first, the second is a joke but it does make it more interesting since they are paying for only a room which opens up temptation, don't fall for it. The first thing I would do is issue an official notice stating how much they owe as well as a lease termination and if they don't pay it within the period prescribed by your state and leave they are being evicted and or sued in small claims for the past due rent. The second is let them know that you fully intend to go through with the eviction however if they can be out by next Sunday you will cancel and forgive all debts. You aren't going to see the money anyway but remind them that finding housing after this is going to be next to impossible and staying is just kicking the can down the road which may be a long one for them with an eviction on their record. If this doesn't work then file the eviction and be sure the proper documentation has been served officially. Since they are only renting the room you are able to have your brother move on in, if possible have another sibling move into the 3rd bedroom as well mostly just for a second set of eyes. Go through the process and don't fall into the temptation to fall into a self help eviction and end up having to pay them money. If you all don't move in I'd install locks on the doors to empty rooms with cameras you can monitor remotely, you don't want them moving in any extra people or having extra space to damage.
Part 2 the fun one: Don't do this.
They are only renting a portion of the house, still have 2 or better all 3 siblings rent the other 2 rooms. Still file the eviction but a persistent reminder to leave at every passing, maybe even one of those retirement countdown clocks until the eviction hearing. The common area is for the common good make sure you all get to enjoy it. Does anyone like anything weird because maybe you could share your interests on the common tv. Everyone needs basic nutrition and the average American is deficient in many nutrients that can be found in fish. Cook plenty and don't be so picky with your leftovers where you are free to microwave them for a quick on the go bite on the way to wherever you are going to get out of the house. Same with broccoli and brussel sprouts that stuff is great for you. You may also want to broaden your pallet and experiment with certain ethnic dishes. They have decibel readers on Amazon and counties have noise ordinances, don't go over them but it is not illegal to go right up to them. If parking is at a premium, make sure that you all are getting the best spots. What does your state/county say about hability standards and temperature because a nest thermostat may help you all pay utilities if they are in your name, don't go below or under the legal limit and don't risk your pipes. Also, a lot of hot water heaters can be turned down where there is still hot water but not a lot to save the environment and your utility bills.
Really though it is fun to fantasize but keep it at that and it sounds like this person is either in a bad situation themselves or taking advantage of yours. File the eviction and the process there aren't any shortcuts outside of cash for keys which is another avenue. Is this person working because this may be the route to go if they have no income and no ability to leave but assuming they are working offer the clean slate leave first and see what happens.