Thank you so much for your speedy response!

First of all, I tried to check the potential miles earned with each program and got the numbers with BA easily but could not find the equivalent with AA.

I apologize for not being very clear in my original post, but I do not have any intention to change the airline carrier, just the reward program the miles will deposit into. To explain further, I was looking at her itinerary online and saw where you can add your frequent flyer number and then learned that it could go directly into her AA account. Unfortunately, I chose AA prematurely, and now (with the help of your advice) would like to change it to the BA account I created for her. I couldn't figure out how to change it online, which is why I'm concerned that I can't change it once it's been decided. I'm actually on hold with BA right now (have been for 17 minutes) to see what I can do. Who knows, you may read this before I even get through!

I hope that clarifies my situation.

Also, she will be traveling with her daughter that is under 18- will they be able to collect her daughter's miles despite the age constraints?

Thank you very much for your help!