Sorry this is rather long. I've become too invested!
The relationship has obviously broken down well beyond repair, to be honest, so I would split at whatever financial cost.
I'd be more concerned that he'd use his supposed role as "primary carer" to expect full custody of the children and subsequently higher alimony.
That said, if you forced him into that position could he actually be bothered to provide a home for his children if it meant he actually had to look after them?
Interestingly the FCFCOA website says that spousal maintenance is to be paid when the spouse is "unable to adequately support themselves".
It also says that both parties have an equal duty to support and maintain each other as far as they can.
It shouldn't, in my non-legal opinion, mean that he gets to walk away with no responsibility but be paid for doing nothing.
I'd look into the phrasing of the spouse being "unable" to adequately support themselves. If he got off his arse and got a job he'd be able to look after himself. He's not unable to work. He's unwilling.
A few websites I've seen say that spousal maintenance can be for a fixed period of time to allow the financially disadvantaged spouse time to improve their own situation.
It also says that it's calculated on a variety of factors including the age, health and earning capacity of the party seeking support, as well as the care of children from the relationship. The fact that you pay school fees for your SEND child should therefore be taken into account in terms of your own ability to pay him.
I'd definitely get a second opinion from another family lawyer.
In the meantime, I'd start giving him a list each day, by text or email, of everything that you think should be done in the house each day. Then when he's not done it, send a text the next day, and the day after that.
You're then starting to build up a paper trail that may be able to be used against him to prove that he's not fulfilling the standard SAHD role. Not sure if it would be useful, but there's no harm pointing it out to him. Hopefully he'll get fed up with the nagging and leave of his own accord!
I agree with others to stop doing anything that benefits him directly. Cut costs to TV services that aren't necessary, stop doing his washing. Make him live like he lives alone in his own home.
I'd also give him a deadline. "Sort yourself out and get a job in 6 months or I'm divorcing you". I suspect even if he does get a job in 6 months you'll still divorce him, but at least if he gets the job you'll not have to worry so much about the alimony!