Val65, from reading your post, I'm assuming that your GS hardly ever sees his other GM, except for birthday/Christmas.
So, for her to expect him to be comfortable going to her for weekends is unrealistic, sounds like he hardly knows her, and she hardly knows him. You would do right not to allow this.
However, if the other GM is serious about wanting a future loving relationship with her GS, and she can be reasonable, in that she's willing to work towards this, then I can only see that as a good thing. But you first need to ascertain exactly what her intentions are. She can't just dip in out whenever it suits her. And things need to move slowly. She can't expect to go from having very little contact with the child, to suddenly having him for weekends. Best to invite her over regularly, just for coffee/chat to begin with, then progress to shopping trip/lunch, and something that's enjoyable to your GS, such as a trip to a park/cinema/etc.
She needs to gain his trust gradually. And maybe, in the future, they'll have a good relationship. But, as I assume you are his main carer right now, and you know your GS well, then you are the one who pulls all the shots.