Betty if they get to the end of lower 6th to be honest I'd think seriously about whether you could wait to follow him until after their A levels are done. Maybe you could do a 'staggered move' (Eg husband relocates for work in Aug next year, starts working while living in a flat, you and twins follow him after their exams are over in the following May/June) - I know a lot of expat families who've done similar. Another alternative is them going to boarding school for 6th form, not that I'd suggest that to be frank!
A levels and IBs aren't interchangeable, so if they're halfway through A levels they won't just be able to slot into IBs. Could you start them doing IBs now, where you live in the UK, if you think you will be somewhere they could complete them in California?
California (as a state) is pretty broke; it doesn't have a very good taxation system (weird property tax rules) and so it has a shoddy tax base, and that has affected funding for state schools and universities. I do know that its state universities (UCLA, UC SoCal etc) are laying off instructors left, right, and centre, but if your daughters are willing to trek further away from home around the Pacific Northwest (Great universities in Washington state, also you have Canada, there's Vancouver up the coast...) that's an option. It may be that if you stay in the UK so they can finish their A levels, they want to stay there to go to Uni as well... which could be easier for them, certainly it's an easier applications/funding system to navigate if you're a Brit.
SATs aren't hard, exactly, but they do require some things (maths, for example) which I gave up with relish after GCSEs and would have hated to be tested on again aged 18! They would also have to crash-course learn a lot of American history and possibly some aspects of some sciences which are covered differently in the GCSE syllabus. And, of course, there's a technique to taking multiple choice exams successfully which the UK school system does not prepare pupils for.
Sorry this sounds a bit DOOMy, it's by no means impossible to move someone for the last two years of high school, which roughly equate to sixth form (though it's uncommon). High school over here is 4 years, from year 10 onwards - so they would be walking into gangs of people who've already made their friendship groups. But that's the same all over the world, and frankly as exciting novelty Brits they'd probably have a great time! I hope some of it helps.