Am I being irrational?

My SO's father is "dating" someone, they've been together for a couple of years and she has 2 young kids. Our son is 6 months old. We never see her she never speaks to us or asks how hes doing but the rare occasion we do see her with SO's dad she takes a million pictures and posts them on fb calling him her grandson, and calling her kids his aunt and uncle. I could be going full mama bear but it pisses me off to no end - I just want to be like you are NOT his grandmother. The fact she doesn't generally acknowledge us directly makes it even worse. She shares my posts of him with captions of grandbaby and blah blah (thankfully have it so even if she shares only mutual friends can see it). Hubby tells me to do what the rest of the world does and get over it. I don't want my baby being confused when he's older. I don't want him calling her grandma or whatever cause she isn't. Am I being irrational? Ugh it just bugs me to no end.