And we have another "snakes in a restaurant..." No, this isn't remotely normal and needs to be corrected now. If it isn't stopped, it can only get worse. There are dozens upon dozens of threads here about the ways that in-laws can trample the parents (and others) when it comes to grand kids.
This is not normal, reasonable behavior and as a grandchild with a grandparent who did this, I can tell you from experience that this *will* cause some serious problems later and probably is already.
The parents need to set boundaries *now* and let these two know that number one, the *parents* will decide who spends time with the baby and when and number two, not respecting these boundaries will result in less grandchild time or a cut.
Trust me, once this fence is trampled, it's a domino effect. My grandmother pulled this garbage with all of her grandchildren and to this day, there are serious rifts stemming from it.
But to answer your question, no, this is not normal.