The FAA is strict about the 2 year cut-off for "lap babies". The burden of proof is on the parents to prove that the child has not yet had his or her 2nd birthday. Many airlines ask for the birth certificate but I didn't see this mentioned on UA's website. You will probably be asked her birthdate at check-in.

http://www.united.com/page/article/0,6867,1051,00.html

Once we did have a child over age 2 without a seat. The mother didn't speak English and was returning to Africa. Her child had turned 2 on the trip. We believed she was just misinformed and not trying to get away with anything and begged the ground staff to remove an employee to accommodate the child. We couldn't risk keeping the child on her lap as that would have been a FAA violation and we could have been personally fined.

If you are caught, you could end up paying the full fare for a place or removed from the flight.

Perhaps there is someone she can stay with there in Denver while you attend the wedding?