Baby and Luv have given good advice and I will piggyback off of them.
Here's a curveball tooge. In our culture in America too many families let the wife lead the way,way too much and clean up all the messes(literally and figuratively) and especially when Dads are very pissed because Mom doesn't want Dad to lose his temper and the relational politics are not ruined. Women in general avoid conflict and it is very easy for them to smooth it out without real resolution and men in general just want to fight thus resolution is avoided as well.
However, you are an adult and you were wise enough to calm your emotions. I think both you and your wife need to show a united front with 'you' taking the lead. There is nothing more refreshing and desired by a wife than a husband who truly takes the lead for the family in most things good or bad. Men have gotten lazy in our society and let the wife pretty much do it all. Now I am not saying you are like this whatsoever but if I'm reading between the lines correctly here you not only want to be a part of this resolution but you actually want to take the lead because this is your little girl !! Correct ?
This is what 'real men' do and
it will do wanders for your relationship with your wife as well as your family and you will find surprisingly that leadership is how we as men are wired and it feels more comfortable and more confident as time goes on if you are not doing this already. Again, I'm not saying you have this issue, I'm speaking in general here.
Just a thought
