This should be an easy decision: Your daughter should apply REA to Stanford and apply as early as possible to her second choice, which I understand to be UCLA.
I think that many kids who apply early to Stanford are making a mistake because applying early to Stanford they may not apply early to other private schools. Many of these kids have no realistic chance at Stanford, but might have a shot if they applied early to (say) Dartmouth or NYU.
I was at a session a few years ago held by the dean of admissions at MIT for faculty and staff. He said that most schools are not honest about the advantages of applying early. He said that you virtually always get a boost by applying early. Sometimes the boost is minor, such as at MIT or Stanford. But sometimes the boost is major, such as at Penn. (These examples are mine, not his.) The reason for the boost is very simple: Schools are fixated on their admit and yield rates. When a kid applies early, both of those rates are likely to go up.
If your daughter’s second choice were Dartmouth, I would say she might be making a mistake applying early to Stanford. Frankly, with her board scores, even being a legacy it might be a stretch. (I obviously don’t know the other details of her applicant.) But given that her second choice is UCLA, she can have her cake and eat it too.
You keep mentioning that the applicant pool is stronger early than regular for Stanford. That may be true; I have never seen any statistics. But there are statistics that the admit rate is far higher for kids who apply REA at Stanford than for those who apply regular. I think it is about 3 times higher (about 10% v. 3%).
There is also a belief that if a legacy doesn’t apply early but applies in the regular round, it means that the legacy isn’t really interested and is just applying to satisfy Mom or Dad. Makes sense to me.
Unless your daughter’s preferences change, my very strong recommendation is for her to apply early to Stanford and really stress the dance, and to apply as early as she can to UCLA. Both are great schools. Best of luck to her!