Gardyloo: for an AA plat challenge, to my knowledge ALL qualifying flights need to be on AA metal. However, she would qualify as regular AA plat after 50k miles (and I think 4 qualifying flights on AA metal). One quick deeply discounted return from home before the trip would do the trick, although she would be a few thousand points short. If she were to be flying at least 6500 miles on AA metal, then a plat challenge would be the best way forward. She could then still credit all the BA and other flights to BA, which might get her enough TPs for silver with BA (not that having both is much of an advantage).

For BA, also need 4 flights on BA metal. So although she would have more than enough TPs for silver, she won't go up a tier until the 4th flight hinted at by the OP. By which time, all excess TPs would be wiped out. A bit of a shame.

Earn/burn rates are better on AA, they have lower fees, but to retain AA plat/EXP requires rather a lot of flying, which may be difficult for a leisure traveller. BAEC has the advantage that a leisure traveller in premium cabins can make it to top tier (just about, perhaps with the odd AA F/KUP fare).

Of course, if MFU is really desired, a few miles can be thrown to BA, just enough for MFUs (which would in turn, earn some miles), with the rest still going to AA.

tb