I wouldn't get too upset by it. FaceTime can be a real nuisance, IMO. I hate it, and I only answer if it is my daughter, and even then I turn my phone so that I'm not visible
. I find it incredibly intrusive, and know others who feel likewise.
I'm someone who (whilst being very sociable) really dislikes the idea of people 'dropping in' unannounced, and think that FaceTime is on a par with that. I want to be able to relax in my own home without feeling that I have to be 'visitor ready' at all times, and that I have to be available whether I want to be or not. If I also had a 10 month old baby I would feel that even more, yet arranging a call would be difficult to organise around a baby's mealtimes, naps and so on.
Maybe when he's a bit older and has more of a predictable routine your DIL might feel happier with it, but if you pressure her at this stage it could become a problem. My advice would be to back off for now, and not to take it personally. I understand your feeling upset that the 'other granny' gets to FaceTime, but that could just be because your DIL can't say no to her mum.