I think you were correct in changing the ticket. I once booked an award for a friend as Kathleen while her official name on her passport is Kathy. CSR suggested that it might be a problem, so we changed the ticket.

In your case, I would write a letter to UA, complaining about having to pay the change fee to correct their mistake. Be polite, but stress the problem arose because of difficulty in communicating with the CSR at the ICC. You might get a voucher though, instead of a refund.

In the end, changing the ticket was the right thing to do, giving your mother one less thing to stress about on her trip.