We bought rt tickets on United for a Christmas week trip. They have changed the return flight twice, with the most recent change including a connection that departs 9 minutes before we are scheduled to land from our first leg. Here are the 2 options we were given: stay on that flight & when we miss the connection, the gate agent will "probably" give us a hotel voucher as it is the last flight out that night. (Did I mention this is New Year's eve?) or take a different flight home the day before.Our lodging is paid for the week, we won't get a refund if we leave early. Anyone got any suggestions as to how to handle this?