ANSWER - This is a very hard question to answer because of the sensitivity of your personal circumstances. However I have given it a good deal of thought and I do have some suggestions for you.
Before we explore anything to do with magic I want to look at the practical possibilities first. As a witch, magic is very often my first port of call but by no means is this exclusive. In solving any problem we need to look at the most effective methods at your disposal and these will include both the magical and the mundane. In situations as serious as this I am always loathe to jump in straight away with spell work as I believe I have a moral obligation to first point out the different people who will be able to give you tangible help to get you out of the situation you are in.
So - mundane first. You don't say if you are UK or USA based but whichever part of the world you are in there is Childline or an alternative number where you can speak to qualified professionals who can give you advice and support on how to manage and leave this situation. These numbers are entirely in confidence.
ChildLine (UK) http://www.childline.org.uk/Pages/Home.aspx Call 0800 1111
ChildHelp (USA) http://www.childhelp.org/pages/hotline-home Call 1-800-4-A-CHILD (1-800-422-4453)
You don't say if you are still in education but if you are your teachers/lecturers will have access to help groups who can assist you and your mother to get away from this bully.
There are also refuge centres for abused women where you can both go if you feel threatened. http://refuge.org.uk/ 0808 2000 247 (24 hrs) will be able to give you advice on how to get placement in a refuge. The Domestic Violence helpline in the USA does the same thing http://www.thehotline.org/ 1-800-799-7233 | 1-800-787-3224 (TTY).
Your doctor will also have information on local support groups as will your local police station. Both the police and your doctor will respect the information you give them and treat the matter in confidence.
You say that this man is lacking immigration paperwork but that you are reluctant to call the helpline because it will be obvious it is you who has done it. I'd like you to consider your concern with your mother and this man knowing it is you who has made the call. From a safety point of view once this man is out of your lives and deported he is no longer a threat for you so in tipping off immigration you are not putting yourself at risk. If your worry is the fact that your mother will blame you I doubt she will blame you for very long. You have every right to put an end to a situation in which you are being abused and you would be doing the right thing in helping to put an end to the abuse of your mother as well. Even if initially she is a little taken aback at what you have done, I have no doubt she will eventually come to understand
why you have done it.
I'd also suggest it is likely that your mother would be grateful if you took decisive action on her behalf. Often women in violent relationships are too frightened to take any steps toward leaving the abusive partner. You sound like you have the strength to do it for her.
And worst case scenario - she's angry with you. Sometimes the right thing isn't necessarily the course of action everybody agrees with. In getting rid of this man you may potentially be saving your mother's life. Find the strength in yourself to do the right thing not the thing other people want you to do. And consider the regret you will experience if you do nothing and this bully does end up going too far. (Choking incidentally can go badly wrong and end up with fatal results even if they are not intended. This is serious abuse and needs to be stopped).
You say you have elder brothers. Do they know what is going on? Could you talk to one of your brothers and get them to come to you sooner?
Finally, from a mundane perspective. You actually hold the whip hand in this situation. If this man is found out to be an illegal resident, as you say, you could potentially get rid of him very easily. Depending on how you judge the safety of this course of action - you know this bloke, I don't - you could sit him down and tell him calmly that if he raises a hand to you or your mother again you will phone immigration immediately. Its a direct threat, certainly but there is a lot of truth in the old adage that bullies are cowards. If he sees the sense in what you are saying he may well back down. If however he is a uncomprehending idiot then such a course of action may put you at risk.Make the call based on what you believe to be the safest course of action.
I'd also suggest you have a frank talk with your mother. She may well be willing to suffer for her own sake indefinitely but if you tell her you are frightened of this man that may stir enough of a backbone in her to kick him out now. Its worth a try.
Ok, so that's my mundane advice. And that is also incidentally where a lot of people would stop giving you advice. But I always work on the basis that when people write to me they are looking for a witchy perspective (why else would you write to a witch on her witchcraft website ...) and as magic is not something I play at and I do consider it a tangible and reasonable method to deal with most issues, I am happy to offer advice from that perspective as well.
There are two steps to the magic you need to take. The first is to disarm the man and make him less of a threat to you while he is still in your home. The second is to get rid of him entirely.
We will start with a simple binding spell. Get some of this man's hair (try scraping under his razor blade) and then mould a simple plasticine (or wax/clay) figurine of him. Nothing elaborate, keep it a simple person shape. Personalise it by carving his name (the name he is known by if it is different to his birth name) onto the centre of the figure (poppet) and pressing the hair into the poppet. Next, find a piece of string and physically bind him. (For a malicious working I like to tie the string very tight so it warps the shape of the poppet and squeezes him out of the recognisable shape of a human being.) While you are doing this, visualise him squirming against his bounds, unable to escape and powerless against the confines you are placing on him. State your intention clearly - "I bind you so you are powerless to cause further harm to my mother and myself." Then seal him in a jar filled with salt (I rather enjoy pinning said victim to a cork board with long needles but the jar will work better for the next stage).
Now you have your bound poppet in a jar you've bought yourself some time. The next stage is to start to make this man disappear from your life. Once a week, open the jar and with a pair of scissors carefully snip a small amount from the poppet (say 10%, the idea being that when you have done this ten times he will be gone). Don't worry you will physically harm him by doing this, I know the films show poppets as literal representations but the magic we are doing here is very different. Burn the piece you remove from him. Complete weekly, snipping the same amount off until the poppet has all been destroyed and burned and the man has gone from your lives.
I do have to add a caveat. Spells work with intent and the best way to effectively demonstrate intent is to take practical steps alongside your magic. (I've spoken before about how my weight loss spells don't work when I don't bother eating less as well. Same kind of thing here.) Use the practical advice I have given you in tandem with the magical advice and you'll get the results you want. But take control of the situation and step up the mark, you can't afford not to act. Cowardly violent men will only become more cowardly and more violent. I've given you some time to decide what you are going to do. Make sure you do something.