How exactly do you know what she would or wouldn’t have agreed to? She readily acknowledges that her oldest daughter has more than her younger siblings, and that she isn’t going to deny her those things.
“My elder daughter has lots of opportunities that the younger two don’t. If they ever comment on this in the future they will of course realise that it is because they have different dads.”
The piano is there specifically to facilitate the daughter’s interest in music, and the rest of family have, up until recently, left it alone (and even then, it was just the younger daughter who briefly used it). Does OP say outright that she knew it wasn’t to be used as a family piano from the beginning? No, but what she does say suggests she knew this was the case.
“My ex has facilitated her music and has bought all of the instruments and paid for lessons…Elder daughter has locked piano as her dad has instructed that my younger children cannot use the piano or have use of the other instruments.”
She also refers to it specifically as her piano. Not ‘their piano’, or ‘our piano’. Her piano.
“I will not disadvantage my elder daughter as so many people think I should by getting rid of her piano”
“I think my elder daughter would prefer that her piano is not shared but wouldn’t have challenged me in this way unilaterally.”
She also seems to have become aware that this is coming from her daughter, via her ex:
“I do hope that this will work out in a year or two when younger daughter becomes older and more proficient and maybe elder one will be less precious.”
She knew her daughter didn’t want to share the piano, but assumed she’d get used to her sister playing it, or at least wouldn’t feel able to object.