As Jamie Cox commented, you would do best to work to categorize your mother's matches. Working with her matches is better than working with yours for the purpose of identifying her father because a) she will have more matches among the relevant people, and b) for some of them, they will be stronger because she is one generation closer to them.
So, categorize her matches as those you are sure are from her mother's side and the others. Her mother's side matches you exclude from further consideration, even though there is a small possibility that she might be related to a match via both sides.
The "others" category will include essentially all from her father's side, but it will also include some from her maternal side. Absence of a match is not proof of an absence of a particular relationship (other than for very close relatives like a parent), and additionally there are matches which are maternal but not in a way you have knowledge of.
Look at the strongest of the "others" matches. You will need tree information for those people. You may want to research your mother's maternal side in more depth to see if the remaining matches actually belong to that side. Collect the ones still potentially paternal and try to find where they're related. If you're persistent and lucky you may eventually perceive two groups of related matches, and find from the tree information or further research, that the two groups are related to a male who could be your mother's father.