I hate it when non-lawyers throw out legal terms like pain and suffering - does nothing but put the reader on defensive. I agree that OP should get reimbursed for the rental but not get a cent or skypeso beyond that in compensation mainly for being melodramatic...

And if the engagement was so important, then perhaps OP should have booked an earlier flight, or planned to arrive in TUS far in advance of the last flight of the day to ensure she could make her appointment. Delta should not have to compensate individuals for poor planning.