While United clearly didn't handle the affair very well, the mother might want to reflect on what would have happened to an unrestrained 12kg child in the event of a RTO.
Dave, you have a point, but the standard procedure for under-twos is sitting on a lap and being held.
I first heard about this incident on CBC's As It Happens and the mother came across as very rational. What staggered me is that she said that a United supervisor told her after the fact, that she should have put the seat belt around her AND her child!
I don't know about the FAA rules, but in Canada, TC rules explicitly forbid doing that. Common sense tells me the same thing.
Ironically, my daughter flew from Los Angeles to Vancouver this week, with my granddaughter on her lap. They were going to Vancouver to celebrate her second birthday, so on the way home, they've had to buy a seat for her!