Be authentic. Do uncomfortable work. Surrender the outcome.
If you do these things, you'll find happiness and contentment in any endeavor, including relationships.
Like Zap said - you can only control your own actions and reactions. Speaking clearly, acting clearly, and recognizing that all you can do is run the play - the outcome is beyond your control because it involves other human beings.
Women aren't attracted to "alpha" males because they put their foot down and control things. They're attracted to men who have their shit together and don't waste time worrying about things out of their control. It represents a grip on reality, and a comfort in their place in the world. Most will respond positively to you being comfortable in your own skin - those who don't give themselves away as people you don't need in your life on a regular basis.
Be the rock. Don't say always and never. Do everything in your power to keep the lines of communication open and free of judgement. Loving yourself and being honest about your own flaws will go a long way in conveying compassion and empathy in a lover's quarrel. The universe is just constant destruction and chaos - look past your little corner of earth for some perspective. The best thing you can do is reduce the amount of suffering you and those around you endure. Don't pay attention to social norms, and virtue signaling from those around you - be honest with yourself and your family about what will reduce as much of that suffering as possible.
The best version of a father for your daughter is one that is content, consistent, graceful, and loving. If you can't be those things living under the same roof as her mother, work to resolve that in the best way possible. Deciding up front how you want the chips to fall will result in unmet expectations, and more suffering. Do the work, be honest, and let it ride.
Life as we know it is way to insane, awesome, and ridiculously rare to be wasted suffering internally day in and out. I hope you find a path out of the darkness you're in. You've got a pretty good light to lead the way in your daughter.