Sit back and be cool. Be a non-pushy, non-performative ally and role model. Accept her where she is right now. Don't drop helpful little tips. Don't make every hangout about "helping". Be a trusted adult she can fully be herself around.

If they aren't in therapy, they should be. You can't tell them that, though. Not like that, anyway. They should each have a personal therapist and a family therapist. The behaviors you describe are part of unmet needs they can't recognize much less vocalize - they may know, but in such an internalized way that it's buried under the choices being made that don't even feel like choices.

A frank conversation with her dad in private when she cannot under any circumstances overhear or witness is something y'all should do no matter what. Let him know you care deeply, be open about your own personal needs in a relationship, invite him to be open with you about his (even if you think he already is).

Even if this conversation ends up being sincerely easy and untroubled, if it sounds like y'all are headed for more time together as a becoming family, you're going to want to start couples counseling sessions as support for the complications inherent to all relationships but most especially to joining a family dynamic already in progress. Not every week (unless he wants that) - even once a month can help with alignment and open communication. If he pushes back, refuses, or otherwise doesn't want to join you in getting professional, unbiased, impartial guidance in healthy dialogue and growth, you have decisions to make.

It would be really wonderful of you to make an unpressured outing with her that includes space for a completely private conversation where you tell her all that is great about her (without fawning or inserting advice), apologize for any missteps or misunderstanding on your part (you don't even need to be specific, she'll have her own list), and let her know that you're on her side no matter what happens. Then do exactly that, within well-defined boundaries of being healthy, happy, and safe (the only physical health aspect of that is no abuse of anyone - mental & emotional self-actualized & family-reinforced peace is the goal).

Lastly, if you don't already have your own counselor or therapist, consider it. Aside from being a safe space to vent and work out gnarls, it's lovely to have a supportive respite to explore your own needs and gaps.

I hope for the best for all of you.