Nobody seems to be thinking about the harm being done to the OP’s daughter. The piano was a gift from her father to her. It was not a household gift bought by the OP for all the children to share if they decided to learn. That matters.
The only harm being done to the OP’s daughter is the division being driven betweeen her and her siblings, by her father.
That is far more damaging to her than her little sister having a 30 minute lesson twice a week on her piano.
Which would be standard in any other family.
Its not the OP's father that is being controlling here, it is to OP by trying to force her daughter to share gifts from her father. The fact the piano is in the OP's house doesn't change who owns it or why is was bought.
Trying to frame it in this way is really sinister of you, and peak gaslighting.
The OP needs to think about ALL her children, as any other parent does.
The fact is that the eldest DD is part of a family and this is how families work.
There is no other situation I can think of where a child, in a multi sibling household, would have a piano for their sole use.
Or where a child, in a multi sibling household, would have a tampoline for their sole use.
Or where a child, in a multi sibling household, would have a playhouse for their sole use.
Or where a child, in a multi sibling household, would have a puppy solely for them - with no other children being allowed to touch it.
Regardless of who bought the item.
THAT is what is damaging to children. The OP’s daughter is old enough to understand.