I have always been a father to my daughters. Even now they call me dad. Sometimes it is awkward, but I am always proud to be their father.
Perhaps as Donna said, the awkwardness is because of the language we speak. My daughters will often refer to me in the feminine but with the honorific of father: "My dad, she..."
I made it clear when I transitioned that I did not have any intension of usurping their mother's place. I did not want to be called "Mom". I could never do that. But, I felt that I did not belong to the fathers day crowd any longer. So I asked that I not receive any Fathers Day cards or gifts. And for Mother's Day all the women in our family celebrate that day together. We exchange cards, and have a dinner together that celebrates the maternal in all of us. Two ex-spouses, two adult daughters, a lovely granddaughter, my partner and myself. It was lovely.
Besides, Mothers day comes first!
About the only one who perhaps suffers in all of this is my wonderful son in law. He knew me for several years before I transitioned and we were the only two guys that celbrated Fathers day. Now he is the only one. But perhaps that is good because he is celbrated as the wonderful man that he is. He never questioned my motives and wants me to be happy. To his credit he has NEVER made a mistake in my name or pronoun. I love that man. My daughter is very lucky!
I will celbrate his Fatherhood this year and be happy that my daughter has a wonderful husband, and my granddaughter and a wonderful father and my yet to be born grandchild is going to be born into a loving extended family.
-Sandy