“Dad” (interchangeably either one)
Use different father words as per family preference. These could be variations of the same family word, like dad and daddy or papa and pops, or entirely separate words like dad and papa.
Use the dads’ first names, either with a father word or without. I know some people who call their grandma “Mama <name>” because she acts like a second mother; no reason it couldn’t refer to an actual mother. That happens to be a non-English example, but it could have been in English. Similarly, I know someone who addressed his (unfortunately now-deceased) parents by first name with no parent word, in English, even though he had the conventional pairing of a mother and a father.
Lots of solutions.
Then for my grandmothers, they were both "granny" but I included their name (first name for paternal, last name for maternal).
It's not an "issue" for parents, exactly, but it is an interesting choice because of how much less trodden a path it is. Would you both go by dad? Would one or both be daddy, dadda, or pop? Would you use first names or diminutives after a certain age?
It got out of fashion though, not really common anymore at least in my circle.
Sometimes it feels like we've found a fence in a field and started tearing it down because, today, we don't want it to be there, but I'm not as confident as I'd like to be that there wasn't some reason the fence was built that we haven't discovered yet. I'm not confident that there is, either. I'm just apprehensive about trying to change something in a few generations that developed over millennia.
Are we definitely more astute than the way the planet and the universe directed human development? Maybe. But also maybe not.
Option one: The winner becomes <dad|mom> Prime.
Option two: The loser gets to live with not <dad|mom> for a year. Or runner-up.