@eminyan
he can better himself and admit his mistakes
If he betters himself, admits his mistakes, and does at least the minimum of the
remaining actions available to him as a Dad (i.e protecting/supporting her from the shadows since she clearly doesn't want anything to do with him instead of supporting her openly, intruding on her personal space)
That itself is considered redemption.
Redemption does not mean the girl has to forgive him and be a family again, nor does it mean erasing his sins.
As long as his character moves on from "Grade-A Abusive Asshole" to "Was once an asshole, now a moron" its "sufficient" redemption (sufficient being subjective).
Whitened Chocolate Milk's (I'm not a bad person just because i can use darkness LN)
is one example of "somewhat redeemed but not forgiven". This dad here can reach this state at best.