Can I figure out the identity of my grandparent from this information?
One of my potential grandfathers had blue eyes, so if it had been him my mother would have received two blue eyes genes and have blue eyes.


No, this does not necessarily follow, because eye color genetics are more complicated than just one dominant-recessive gene. See, for example this article from a someone at  Stanford University on How Blue Eyed Parents Can Have Brown Eyed Children. It isn't common, but apparently it does happen. 

Solving your inheritance just based on eye color with 100 percent certainty is not possible.