In my youngest grandsons case the other granny and I get on pretty well, he lives abroad and I visit once or twice a year, other granny lives close by to him so sees him all the time and often takes him out or babysits picks him up from day care, even giving Mum and Dad a week off for a trip.
When I go out to visit we make a point of spending time together either with the little one or on our own , we take him to the beach or pool and its then the pangs of the 'green eyed monster' rear up when I see how happy and lovely their relationship is but I push it away because I'm really glad he has such a lovely lady looking out for him.
I've had to come to terms with the fact that I'm never going to be the hands on granny I've been with my other grandchildren with this lovely boy and its pleasing to me that he has the other granny who will always be there for him and is generous enough to message me on FB with pics and titbits of things she's done with him..
No granimosity here..