Does the local school have some kind of "welcome" class for new students that don't speak the language? Or at least some support?
My children are- according to DD - "3rd culture kids". I tried to switch DD at age 11 with disasterous results, and ended up moving her back to the international school very quickly. On the other hand, DC3 enjoyed local school and speaks the language perfectly.
How this would work in practice for your DCs would depend on how good the local school is, how nice the kids are, how easily your DC can learn a new language (from what I have seen, children vary enormously in how quickly they can pick up a language, even with the kind of immersion that local school requires).
It also varies with what their talents are. For example, if you have a very literary child who likes to read and is enjoying doing creative writing at the international school, putting such a child into a local system is much harder the older they are. On the other hand, if you have a DC that likes maths and science, it is much easier for the child to be good at those in a new language, rather than if their relative strength is in English.
If you do put them into the local school, I do think it is possible to switch back if it doesn't work. Not ideal, but certainly possible.
As for accountability in international schools, they would be subject to local regulations, and also to the regulations for international schools if they are offering standard programmes such as PYP, or later, MYP and IB.