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Superbat omegaverse (I like this fight me) where Bruce (it doesn't matter if he's an omega or an alpha) is called mom by his kids from the day one. It started with Dick as a joke, but it stayed and was passed down. It was even like a sign for when his kids were mad at Bruce, they would call his name instead of mom. When Jason came back, it took him a while to get him to call Bruce mom again, but when he did he felt the happiness seeping through their family bond.
So when clark was finally part of the family, things started to happen. Clark as always been there ever since identities were shown, and even before when batman and superman were just that. Clark was like their cool uncle, and the one that gives them hugs.
It was, surprisingly, damian who made the first slip up.
Damian: mother, can you sign this paper that the school sent?
Bruce: what's that about?
Damian: nothing that is important, the teacher asked it to be signed.
Bruce: Damian I won't sign something that I don't know what it is.
Damian: *looking incredulous and turning towards clark* Father can you signed it?
*Bruce and clark not saying anything about the title*
Clark: s-sure damian, I can do it.
And from then on they slowly start referring clark as father, bc they saw how he became a permanent figure in their life and how better Bruce seemed with clark now. So now Bruce and Clark are Mom and Dad in the manner.