Yeah it doesn't sound like you'd have any claim on the house if you've moved several times etc. In some ways that's unfortunate, in other ways it's a blessing not to have the stress of a court case.
Do you know if the 17yr old is thinking of going to university? They may not want to live with either of you. You because temporary housing often isn't so great and your ex because he's a knob. They might fund their own way through university with loans and grants and a part time job and not come home in the holidays. I recommend a chat with them because they may want to get a part time job and start saving now, if that's the case.
I'm guessing the 14yr old would pick to stay with you, given your ex's attitude towards the DC. So you're probably looking at a 2 or 3 bedroom place, depending on what the 17yr old wants to do with their life. Consider that if you do enter into a joint tenancy with your oldest, you'll basically be house-mates and won't really be able to throw "my house, my rules" at them any more.
You sound proactive but also deflated. Maybe you didn't take action sooner because you felt ground down by the relationship? He does sound as though he falls short of being a top notch specimen of mankind. Anyway, you are where you are and you're doing something now. There will be a solution to your housing dilemma, you just have to figure out what.
Short term, do you have anyone you could sofa surf with if he literally kicks off the moment you tell him it's over and you find you're out on your ear? You might think he won't be surprised but I wouldn't be so sure. At the moment you've just got a sexless relationship with separate beds, that's a far cry from announcing you'll not do any "wifey" things for him at all any more or pay towards the mortgage and that you're taking steps to move out. He might be deluded enough to think you'd remain with things how they are forever, lots of people do and he might think you're ground down enough to never leave. He also might think you're trapped, since you don't own the house and only work part time. So he might be more surprised than you expected.