The seating problem has happened many time for me when traveling with my family on UA/*A. I now fear traveling with my family since I have to beg and complain to get us together which is opposite of my normal business travel attitude. It doesn't matter that you get seat assignments on the phone. The check-in agent denies seeing anything in the record and waives you off telling you the talk to the GA, the GA refers to the check-in agent.

Request an email confirmation from United. That stopped the finger pointing on check-in. Or pay (as I do for family international travel) for a paper ticket and make sure the seat assignments are printed on them. Ask specifically for this.