"I should probably have been sterilised at birth, or otherwise had a transplant of the bit of my brain that makes life decisions and chooses partners."
hobbgoblin, it's sad to hear you say that. Even though the chorus is all singing: "No!" "Get your own solicitor!", etc, people aren't having a go at you for these problems. You don't have to feel defensive.
It is amazing what sort of crap becomes "normalised" during a life of it. You are probably just rather shocked to hear how bad it sounds from the outside.
So, to recap some of the excellent advice on this thread (I can't hope to replicate anything about cars!): this is not a good deal, as it is short-term, insufficient and could lead to your ex's pushing further, to see what else he can not do. You need a solicitor, and it is very shocking to hear you resisting this, or thinking it will cause more hassle for you. Put it this way: if you consulted a solicitor and the solicitor said: yes, this is the best you can do, would he be angry? Of course not. You suspect he will be angry at you for consulting a solicitor because you strongly suspect the solicitor will urge you to fight. You know the reaction if you take this advice, so you want to avoid getting the advice.
However, this is where other posters have had a go, and rightly so. You have to think of your children, and fight for them. Any short-term pain (a bitter fight, relying on buses, etc.) is more than outweighed by any gains you must make, by doing this. What gains? Extra money (as someone said, for your children, for emergencies); a car which lasts you more than 3 years; your self-esteem, which seems to be pretty low.
Please don't say anything again about forcible sterilisation or bad choices. We all do dreadful things, and regret them, and then try to change and do better. You can do the same.