Wondering who will pay bills for our kids if they get sick in their 30s? If chronic disease, will disability kick in?

Depends. Not really a medical question - whether disabilty will help depends on the illness, side effects, employability and if the disability plans have any money (social security being my thought).
Maybe/not. The rules for various programs vary by state and the issues involved. If their condition was stable enough that they could work, this would likely be required to receive any assistance. If totally disabled, there are safety net programs available.