If the DD doesn’t want to share, she’s being rather mean, isn’t she?
Trying to force her to share her father’s/her piano won’t make her want to share, or feel anything other than resentment towards her mother and siblings
Why do you think this? I find it quite a defeatist attitude. It sounds like you think it’s a hopeless task to instil some thought and care for her siblings into the elder DD. Why?
People can change at any age, and a child of this age in particular is at a point in time where change can happen relatively quickly and easily. I wouldn’t give her up as a lost cause.
Removing the piano means that her daughter would choose to spend more time with her father/at her father’s house
We don’t know this for sure, it’s a fear of the OP’s. How much justification there is for that fear is unclear (would the daughter really flounce over this?), but what is clear is the OP is being manipulated into a situation that is damaging the family dynamics because she’s being controlled by this fear. Who put that fear there? . Probably the ex, deliberately, with the elder daughter being damaged in the process.
There’s no solution that doesn’t risk damage to the relationships between them all.
This is the nub of it, and this situation is being created by the ex. Most likely very deliberately.
If OP wants to be a decent parent to her kids, she needs to make sure elder DD doesn’t develop into a spoilt brat with a superior attitude to her siblings, and the younger siblings don’t grow up resentful and feeling inferior.