Just to put a bit of (slightly peripheral) info in to the situation. Twins make a massive difference financially. Without going into a really long speech about why it's absolutely not the same as two children with, say, an 18mth age gap. The expense is unreal. And I say this as the mum of both "singletons" and twins.
I love being a housewife, but it's a good job I do. I could easily go back to work (and did) with singletons. The twins? I can't. Even if I wanted too. And again, there are a hundred reasons why, that I'm not going to derail the thread with, but things that don't even cross your mind (until you are in a "parent of twins" situation) have enormous financial effect.
Someone needs to be the SAHP. Now you've revealed it's twins. If she earns twice as much as him, believe me, they need every penny, he won't have chosen this for the easy life. I know this is of no use to your situation, but I just wanted to add a slightly different angle, as unless you have twins, you can't appreciate the 1000 ways they cost more, need more, the logistics, the time, you just can't explain it.
I'm not saying he's doing right by your DC, but it's likely they have no choice. I love our twins beyond compare, but if I hear one more "oh I know just how you feel, both of mine are under 3" I think I'll explode. It's a completely different ball game. And being real, he most likely has no choice but to be the SAHP. No he can't "just get a job" and if you speak to twin parents who have the time to go into the reality of why, you'll perhaps understand. Again, it doesn't help you, but he couldn't have predicted a multiple birth and all that subsequently entails, also resulting in him no longer working.
The sm isn't going to give up her wage, that she needs to support her own children, and stay at home so her DP can not only bring in far less for her family, but then reduce that further because he's then paying your CMS. Shit, but that's the reality of it. She's not going to voluntarily let her own much more financially demanding twins go significantly without, in order for your DC to slightly gain (I think you said £250 p/m for two children? Less than £10 a day)
It's crap he doesn't contribute. But in the bigger picture, it's less than a tenner a day. Unless you are living in poverty, life is too short. You say 25% of the year your DC are with them. That's actually a hell of a lot!! One day in every four, the SM is covering their costs while they are with her and DP.
I hope your situation is such that you can cope without his shortfall. Our surprise twins have resulted in us changing both our cars, buying a new house, me never working again...all things that we have no choice over, some I like, some I don't, we literally have no choice, it's necessity.