I am not reading through all the responses yet, because I wanted to put in my own two cents. I am very close to the age group of that woman, and speaking strictly as an older person, I think you might have been right in terms of “you got there first and specifically told the woman that this was where your daughter was sitting.” HOWEVER – when you see you are dealing with an older person who is clearly NOT conforming to societal niceties, it is obvious there is something wrong with her thinking, especially if she did everything exactly as you described. You had a golden opportunity offered to you to teach your daughter about derech eretz for the older person, even when that older person does not act properly. Perhaps it was physically uncomfortable for the woman to sit by the wall. I have orthopedic issues that make sitting in some positions for a long period of time, very problematic for me, so I always use aisle seats in shul. Or perhaps she was just an obnoxious, difficult woman. Either way, you missed the mark, IMO.
I think putting your daughter on the woman’s lap was extremely demeaning to your daughter and really an inappropriate response, to say the least. The two of you ladies were jockying for power,and you being the much younger, might have found some type of compromise, i.e., sitting in the middle, as someone else suggested. Sometimes you can win a battle and lose the war. I think this was one of those situations.
P.S. I just read through the other responses. Either Popa is yanking our chains, or he was bullied a lot once upon a time. Either way, Pops, your response IS over the top.