Wow, I have exactly the opposite experience with Piano Adventures. Have you actually used it yourself? Perhaps those students just had 'bad' teachers.
I use PA as my #1 favourite method for most kids precisely BECAUSE it avoids equating a finger number to a note! It very deliberately has students changing fingers on a note, or playing on D-A instead of C-G, right from the beginning. It was DESIGNED as an alternative to the existing middle-c and positional methods.
Yes, it deals with 5-finger patterns, but that's only natural. They're not taught as "positions" (or at least they SHOULDN'T be), but as pentascales. And they are NOT 'stuck' in only those 'positions' as they learn them.
I have found the harmonies to be interesting, not overly formulaic. But at the same time, there is logic in having a certain amount of formulaic harmonizing, so that students can indeed learn what a "normal" chord progression sounds like (so that "unusual" chord progressions are indeed heard as something special). Some methods go too far in trying to make things "interesting" that it loses cohesion for the child's harmonic awareness.
Anyway... I would personally recommend both PA and Celebrate Piano. They both have strengths and weaknesses. I love many many many things about CP, but found there were certain students it just didn't work well with. Like any curriculum, really.

My VERY favourite for young beginners was Music Discoveries by Anne Crosby, but it's not in print anymore... it was just brilliant, I hope she reissues it...
But I would also like to caution about teaching your own without knowing how to teach... It's an odd thing to say as a homeschooler

But knowing how to play an instrument does NOT equate to knowing how to transfer that knowledge to a young child. What to do first. What to do next. What to do if this problem arises. What to do if they don't understand.
As homeschoolers, we'll buy a math curriculum that's designed for homeschoolers, so it has 'instructions' for the 'teacher'. I'm not aware of anything similar for music -- at least not for piano (there are some for recorder).
As someone who has a BMus and MMus in performance, AND has studied pedagogy and taught for 15+ years, I can definitely say with certainty that teaching beginners is the HARDEST part. Teaching intermediate and senior students without knowing "pedagogy" is easy enough -- you're fine-tuning technical details, you're developing expressive skills. Teaching the BASICS, starting from scratch, requires a completely different approach.
Perhaps just this little debate on the merits and pros/cons of Piano Adventures will show you how complex the issue can be.

If you're dead-set on teaching your daughter some little things before starting outside lessons, I'd actually suggest doing book-less stuff. Don't worry about READING music. Just teach her the geography of the piano itself. Start with the 2-black and 3-black key groups (my daughter mastered that at age 2)... go up and down the keyboard playing just the 2-blacks, then just the 3 blacks, in clusters. From there, try playing them individually.
Then let her improvise. You can play a basic little accompaniment in different styles in G-flat major, and let her improvise on the black keys. You can talk about keeping a steady pulse, trying notes of different lengths (drip drip raiiiinnboowwww), loud and soft, high and low.
Let her play with that for a long time.

Then you can start to play with the white keys -- start with D because it's easy to find (between the 2 blacks) and build out from there. But the main point is -- teach her to play around on the piano and have fun, keep a steady beat, eventually name the keys, maybe talk about a good hand position -- but don't worry about reading until you find a (good!!!!) teacher. Just my thoughts.
