When you deal with narcissistic people or people without empathy, you learn quickly that things like unconditional apologies are not from a place of being sorry but from a place of manipulating behavior and actions.

When you cut a person out, you are removing their power over you. They apologize to get power over your emotional state back.

The narcissist doesn't feel empathy for you. The apology is meant as a transaction, not an expression of guilt or an admission of wrong doing.

That's why when you test the apology ("you'll stop this behavior that results in me feeling bad") the test fails.

I think your observation is phrased in a way that implies the father has done something entirely selfless and the daughter has done something relatively selfish.

The reply from the daughter was an attempt to set a clear boundary while also showing appreciation and support for his change. I think setting boundaries like this is a perfectly healthy thing to do, including/especially towards family members.

It was not conditional appreciation. It was unconditional appreciation of the apology followed by rules for relationship.

People are entitled to set and enforce boundaries. Given that dad is abuser, this one is very healthy one, because it allows the daughter to keep her freedom.