Thanks so much everyone for the links and the advice.
My main worry at this point is proving dependence, as we have two siblings in the same country as parents. Siblings are sisters, who are not financially independent nor would it be culturally acceptable for them to be the main source of support -- but I doubt these cultural differences would be appreciated by the canton in way of argument. Anyone have experience with proving dependence in such cases?
Moving back is unfortunately not an option -- it's a catch-22 -- moving back requires a significant salary cut which would then leave us unable to provide for their care.
I do seriously appreciate the concerns on their happiness in moving here, which is why ideally we wanted the permits in place so that it could happen only when it becomes absolutely necessary, but I see that this is not possible. In the meantime they visit 3 months out of the year and slowly build some connection to the country. Dad loves to travel and is quite resourceful in new environments, Mom could care less about travel but is very socially robust and could make friends with a kangaroo! Then again, as of now it is a visit -- mindset might be different if it is long-term. *sigh*
Current plan B is I move back with the kids for some months / years (

), until we can all move to the US where I know I can bring them, and where they also have a strong community, but this would just be a bearable lose-lose situation.