A simple fix is to sell 100 tickets for 100 seats and not more then can be seated.
There is no one more valuable then the paying customer.
You certainly do not tell someone to put their kid on their lap in a already too cramped seat. The VIP they wanted to seat must have been real proud of themselves costing a family the money and aggravation.
At a minimum, they should get a total refund of all their airfares, reimbursement of their next day United airfares, hotel bills and meals, legal fees, plus a hundred grand for aggravation by their employees.................