Everyone will tackle this differently.
My first step would be to contact this match. Not sure I would mention the problem first, more along the lines of 'We have come up as second cousin matches, I'm not sure how we connect'.
If they have an online tree, definitely look at children of their 8 great grandparents. Try to find someone of the right age and in the right place to be your mother's father, your grandfather in the tree.
If they haven't got a tree, or its private, or only mention direct ancestors, you will have to investigate backwards with any names you have.
My only reservation is that, although you probably share great grandparents, you do need to have some idea of whether you are the same generation or not.
My husband's great niece is a match with him at myheritageDNA, any children she had could show up as potential 2nd cousins.
So, in this case, the common ancestor is actually my husband's father, not his grandfather, so you and your mother could possibly be descended from the same person as your match, not a sibling of his.
There are a lot of other possibilities as well.
Take a look at shared cM project
https://thegeneticgenealogist.com/2017/08/26/august-2017-update-to-the-shared-cm-project/Would love to know how you get on.
Regards Margaret