I wouldn't worry about the bit of coffee he gets from his granny now and then so much. But what I worry about is when I see babies being given fizzy cold-drinks, which, as the previous guest said, also have caffeine and also a high sugar content. toddlers and little children should not be given highly sugared things, and also should be limited in their caffeine intake.
I would also ask you, does his behaviour seem to be affected by the coffee? Is he jumpy, or over-excited or naughty? If so, nix the coffee. Your mom must listen to you as his father in this.