FWIW I would send UA a bill for all expenses including the missed nights and the cost of the layover. I would mention that you sent you part of your party to the gate as to advise them of the issue (always possible that the GA seeing many people are going miss the flight could come help at the checkin counter).
If UA does fully compensate you after several tries, the amounts are not so insignificant that I would not hesitate to file a small claims action.