So she was a pedestrian when she was hit (she's OK, but messed up two years of her life). This makes me wonder if it's worth owning some crappy car even if you never drive it, just for the privilege of having auto insurance...
Anyway, yes health covers it but they are first in the line getting reimbursed, even before the lawyer- which I think sucks, I mean what am I paying them for?
The reimbursement right that the insurance company has is called subrogation. The basic idea is that whoever was at fault shouldn't be better off because the injured party had insurance; otherwise it would be rational for individuals to not have insurance as long as most other people do have insurance. Subrogation means someone will still sue you into the ground even if the person you hurt was made whole by insurance. There can be many links in the insurance chain before you get to the person who actually caused the problem, and in your case it sounds like UMC was the final link.
At least, this is the stated public policy reason for subrogation. You are right that your health insurer got reimbursed even though they promised to cover your loved ones, and that feels weird.
Your insurance will cover your children even if they are not listed in the insurance contract. Being redundant to be clear: if a random driver hits a pedestrian child, parent's auto insurance will cover the costs even if they are not involved in the accident. The insurance company may chose to not pursue legal action even if they pay for the costs. The injured party can still do.
Anyway, yes health covers it but they are first in the line getting reimbursed, even before the lawyer- which I think sucks, I mean what am I paying them for?