AITA for defending my boyfriend against my dad?

I recently had a baby with my boyfriend of 3 years, Nick. I work as a nurse with crazy hours and Nick previously worked in a warehouse. When I was pregnant, Nick expressed to me how he wanted to stay at home with the baby at least for the first couple of years as his dad was not in his life and he wants to soak up every moment of our child’s life. We both agreed this would be best for our baby.

I come from a conservative family and my parents were first not too pleased that we had a baby before marriage. My dad has made little hints here and there to Nick asking when is he “going to make me an honest woman”. When I told them Nick would stay at home with the baby, my dad took his glasses off, wiped his forehead and shook his head, but he did not say anything further.

Recently at a family function, my cousin announced that she is pregnant! Everyone was giving her and her husband congratulations. My dad made a slide remark to them saying “talk to Nick here. He’s an expert at the baby stuff”. The comment was obviously meant to belittle Nick and my boyfriend just gave a nervous chuckle and nodded. Later in the day, our baby needed a diaper change, I was in the process of getting up to change him when my dad said to us “woah isn’t that Nick’s role? You do nothing while my daughter works. You can at least change a diaper while she is with her folks”. I had had it. I told my dad to stop with his remarks. Nick is an EQUAL partner in our relationship and he is a wonderful dad who does most of the childcare. I told him just because he did fuck all of the child rearing for me and my siblings that does not mean all men need to be like him and he needs to get with the times because this isn’t uncommon anymore. Things got awkward and mom quickly changed the subject to something else. My dad was pretty quiet for the rest of the night.

After the event, my dad called me saying I disrespected him in front of our family and I was out of line. He said I insulted him as a father and to apologize. I told him I had nothing to apologize for and I was tired of him picking on Nick. My mom agrees with my father that I was too harsh on my dad.