Did some follow up research on this as well: Healthcare.gov is definitely an option! I called their support line can got instructions.
If you, like me and my wife, have private health insurance, no worries: start signing up on Healthcare.gov but choose the option "coverage for someone else." Your relatives will be listed as your dependents for both medical care and taxes. If you choose that they have serious medical concerns (which two of mine do), they will be granted coverage during the special enrollment period. The others can still enroll in Medicaid.
All the best.