In case anyone is interested, I finally got the reply from the FAA. I am going to include a copy of the letter at the end of the e-mail.
I am still waiting for a reply from United. I have been in contact with one of the managers in charge of flight attendants. A couple of weeks ago, she e-mailed me to ask for a summary of what happened during my flight. Apparently, the FA was telling her he simply asked me to move my carseat from a middle seat to the window seat, but that he had allowed me to install it RFing. Unbelievable! I am still waiting for some kind of official apology from United, but I'm not holding my breath. We have another flight coming up in September, and although it will be more expensive and less convenient, I think we're going to fly another airline.
(Having trouble attaching the letter - baby is up and needs to be fed, so I'll be back later).