So a more than 2 to 3 year overstay? Hmmm.... serves her right she could have done more to stay within the law... as silly as it may be it is still the law.
Do.in home country for the trailing spouse thing. Yes easy and will save you doing 800K twice. But the other way is ...use and agent and let them do it all for you.
You can get a vaccine passport from US Printing office then go to where you got your vaccines shots and they will enter info officially. It is a yellow booklet like in the old days. CDC and Homeland State Dept and US Gov approved. Accepted everywhere. Also check if your state issues a QR code for your phone. You can also use that.