I don’t think there’s a standard way to celebrate. But I grew up without my father, so I can’t speak from experience. If I end up having children with my partner in the future, I intend to celebrate him in the same way he will celebrate me as a mother, this assuming he will be a good father.
The sad part about Carrie and John is that he got acknowledged last, regardless of what else they did to celebrate. Once I have a family with my partner, I wanna be first in his life. It might sound selfish but it’s the way I see it, first our family, then his parents, siblings and so on. So I’d want to be acknowledged before his mom on Mother’s Day. And on that note, I would find an acknowledgement of his sister (if he had one) icky to say the least. Carrie had always had a creepy relationship with her brother. Before you come for me, I know it’s platonic and she’s no Cersei, but who the duck calls their brother their soulmate. Their best friend? Sure. But not their bleeping soulmate.
this is the stuff of nightmares 
(That arrow is animated too).