If the mother is talking to the son, then the most obvious reference would be the son's grandfather. Since running a small family business could easily be seen as passing from one generation to the next, again it would seem that it's the son's grandfather who is being referenced. If it is indeed the father's grandfather, then I'd be curious why the position of running the shop jumped a generation. (And that could make for an interesting side story.)
But without further context, it's kind of hard to say. Neither is it clear which grandfather is being talked about: whether paternal or maternal grandfather. Again context could make that clear.
In an intergenerational family, ie., a family where multiple generations live under the same roof, these terms, like jiisan, can get rather twisted and used in unconventional ways. I know that's true in my own family where I sometimes have to explain that "Granpa" isn't really my granpa; he's just the guy in charge of everyone else.
Again, context should make these matters more clear about what was meant. My hunch would be, without further context, it's the son's gramps.