Personally, I don't like the term "auxiliary parent." It suggests somebody who just kind of gets hired in as needed, like a mother's helper or something, not someone with whom "the buck stops." Even "step parent" sounds more related. Not only am I connected to my children by genetics, which has meant that they have many of the same issues that I and people in my family have, but I was involved in raising them from the beginning.
Some families end up calling the transitioned parent based on their original sex and some based on their current sex and some make up new terms -- I'm told that the series Transparent came up with "Moppa."
So far, I'm still okay with being called my children's father (I did "father" them, after all.) I don't have any plans to change that, either. I'm not expecting to hide my history from people I have an ongoing relationship with, anyway, so the idea that my children's father is a woman is only one of the many non-cisnormal things they're going to have to get used to. And casual acquaintances can make whatever assumptions they want. (Insert Bronx cheer.)