First off, your husband does not sound like he's fulfilling his responsibilities to you and his children. He needs to take a bit of responsibility for his half of the equation that is balancing real life demands.
However, you can't change his behaviour, only your own.
Being a SAHP with 3 children (all at nursery or school), with a mortgage and bills in the current financial situation, may well no longer be affordable. If the family finances don't add up to enough to keep you all stable, then you need to change something so they do.
Even if your husband were to get a better job, it probably wouldn't balance the books enough. I'm assuming from his employment history given here that he'd be unlikely to get a high-paying professional career without having to retrain for a time.
So, what else can be done so that the finances balance?
Are you applying for all the benefits you're entitled to? Are you willing to move to a smaller house or one that isn't as nice?
Where do your priorities lie?
If you want the nice house and all the other nice things, you probably can't afford to be a SAHP any more. Conversely, if being a SAHP is more important, then you probably can't afford the nice house any more.
Getting a job isn't the worst thing. You'd still have time with your family and time for yourself, it just means your schedule is different from now. The majority of mums do need to work, at least once their children are at pre-school or school; the financial situation in this country (and most of the world at the moment) means it'd be hard to get by otherwise.
Why not look for something part-time, that either gets you work experience in a field that interests you or leads to a qualification, or that gives you flexibility with your hours to fit around morning routines and school pick-up times? Then, once your children are older, you can use that job as a foundation for more of a career.
You mentioned financial abuse - if your husband is abusive but you haven't felt able to go into detail here, then a job becomes even more important! Having your own income and potential to develop your financial independence means you would have a safety net to leave and still provide for your children. Keep your income separate, going in to your own private bank account.
You absolutely have the right to divorce him if you want to divorce him. Don't let anyone tell you differently.