Your OH must mean a very great deal to you for you to have agreed to live abroad with him although I appreciate that the relationship is fairly recent. Also, since you have yourself moved abroad , you seem content for your own relationship with your GS to be less intense than many modern grandparents seem to want ( or expect) these days( that's not intended as a criticism, just an observation). That being the case is it possible that you could make light of it , rather than making a "thing" of it, and just get him to say to GS "hello chum, whatever, everything OK .... " rather than framing it as building a relationship ?
No offence but given your GSs and OH's respective ages ,is a highly significant relationship for either party on the cards here ?
Agree that given his relationship with his own GC , he does sound as if he wants all your attention and this could be a Red Flag.
Good Luck.