I work in medical collections and I have seen many instances such as this. Major pain in the ass if there is any school insurance involved. I have seen it happen where regular insurance pays, then will take back the payment because the schools insurance should have paid, but didn't, because a bunch of fucking idiots cant get there thumbs out of their asses to do their jobs. But I digress. Here are some suggestions I have.
If the schools insurance is involved or not, be sure to get itemized statements of everything she has done. Keep them forever. If the schools insurance is involved they will need these. They will also need you to be on their ass like white on rice making sure they do their jobs. Believe me I see this stuff get messed up all the time, then it ends up in my office and I have to be a life coach for all parties involved to get the shit fixed.
It would be a good idea to have a power of attorney or notarized document giving you authorization to handle her medical bills. With what all she is facing, whether an adult now or not, she will most likely be one at some time in this ordeal. When she is, you become a 3rd party to the matter, even though she is on your insurance and you are paying the bills. It's better to be proactive and have a POA at the ready because at some point you may need it
Also be sure to have printed copies of E.O.Bs to match all itemizations. Hold on to them forever.
be sure to monitor yours and your wifes credit and your daughter's. When daughter is 18 she becomes the guarantor. I see it all the time where the kid has bills somebody fucked up on and they just assume that oh mom and dad will take care of that...But mom and dad never find out because it's in kids name. Then mom and dad want to take care of it but now they are a 3rd party as far as hippa is concerned. See my point about the POA.
Good luck moving forward. It's shit like this that makes me love my wooden dog ralphie more and more. He doesn't piss in the house, doesn't need walked, and best of all no vet bills.