This is a really difficult situation as you suffer whatever you do. But you honestly cannot put up with someone frequently swearing at you, making accusations, and being nasty. It is abusive, and simply awful to live with. No wonder your MH has been a problem! I’m so sorry you haven’t had the love and support you deserve.
For a start, if you have a spare bedroom or lounge with a sofa, I would go and sleep there every single time he used offensive language and made empty accusations. Every single time, I would say “I am not putting up with you saying unpleasant things to me, I have done nothing to deserve your accusations, and it makes me so unhappy when you are like this. Hardly a surprise I’m not interested in sex when you treat me this way.”
I’m guessing in some ways your OH is jealous of you - you are getting yourself together, spend a lot of time busy with work, kids, self improvement. He sounds totally checked out of the entire family, and you carry it all. But accusing you of affairs is not acceptable, no matter how insecure he is. When he is calm and not wanting sex,I’d try and have a rational conversation where you set out the facts, and then ask him what he wants to do about the marriage. Surely he doesn’t want to carry on for another decade like this?
Meanwhile I’d get my ducks in a row, as a priority, in case the situation deteriorates and you need to throw him out, or he walks out. Have a look at UC and CMS and be ready to apply. Think about whether your kids would be eligible for free school lunch, if they aren’t at the minute.
Make sure you have a separate bank account and save every single penny you can. Think about housing - could you downsize if you have to (I’m assuming you rent.... how quickly could you move to a smaller/cheaper place and would it save much to do so ?) Research local childminders, contact a few and see what it would cost to get wrap around care enabling you to see if you could carry on working full time. Do you have family or friends nearby who would help you out if you needed emergency help with childcare or babysitting while you do college? If not, could you take a break from college and resume a year later? Think about whether work would let you do some flexi hours to help you cope if OH is out of the picture, it’s even possible they’d allow this short term while you are sorting out your family life,
Yes, your kids will be in bits if dad leaves, but if you cope well and there is a minimum of yelling and unpleasantness they will be less impacted, similarly if you can keep positive and show them things will be ok, you’re in control, they will be less frightened. Your OH might surprise you and want some contact with the kids, so be prepared for that too.
Be brave, it is a tough set of choices but you sound very competent. Good luck x