I really feel for your situation. I too have a schizophrenic parent and another who suffered from mental illness but has passed away. I lived with them both until I was 33 and moved away (o/s actually) to get married and start my own family.
The violence in your home is a BIG concern, not just for your mother, but for you as well. As someone in their late 30s, please take me seriously when I say, you ARE NOT responsible for parenting your parents. It is their job to parent you, and it sounds like they have not done a very good job of it. The last thing you want is to remain in a situation that is toxic and could possibly make you sick yourself, if not now, then later down the track. I know your mother cannot help having schizophrenia, but neither is that your fault NOR your burden. And it sounds like your father’s drinking is out of control and needs to be addressed.
You need to get your father’s drinking situation really needs to be addressed, and get support to help you, don’t face that alone, especially if he’s violent. Whatever you do, don’t confront him about it. I would suggest getting in touch with someone you trust (a responsible, mature adult, that is…teacher, law enforcement officer, church pastor, counselor as an example) that can assist you, or call a hotline that deals with alcohol and/or domestic violence and speak to them. Domestic violence is a very real concern and is, fortunately, treated very seriously.
Meanwhile, it is very important that your mother takes her medication, OR, if she won’t, that whoever prescribed it for her is aware that she has stopped taking it.
I know you want to go away on the trip, and as a young person, those kinds of things should be open to you. The disappointment you feel about that trip is only going to escalate into greater disappointments (like bypassing college) if you continue to put the needs of your parents before yourself. I know that is very difficult to understand and accept, but you cannot right what is wrong all on your own. Be brave and reach out to whoever you can.
I know I’ve probably made you more worrisome than not, but honestly, I’m only speaking from personal experience of being 33 years in your situation before my life turned around. Don’t let that be you.
Wishing you the best!!!