Hi,
ok, thanks for the extra details, I've read your msg (outloud) a few times now to 'picture' where you all fit in.

It suggests that the shared ancestor might be found in the parents of your dad's dad (unknown or do you have an idea?).
So these are your great grandparents.
So what you need to do is build a tree for each of your matches persons 1, 2 and 3, going back to their great grandparents (or maybe 2x great grandparents).
For each person, I would think you need to look at their maternal and paternal side, unless you can already rule one side out based on geography (or anything you might already know).
Persons 1 and 2 are going to have trees which don't over lap with one another as they don't match each other.
Look at their grandparents (and possibly great grandparents) and siblings of their grandparents and find out their names and who they married.
It is possible that your dad is a son of one of these siblings.
It's hard to explain but these trees of persons 1 and 2, will meet somewhere and the line where they meet, is the one where you and person 3 will both be on.
(Person 3 is more closely related to you and your half sister).
The tree of Person 3 will possibly, I think, be the line you are on, and will also connect with both person 1 and 2.
It's hard to explain but once you know names, dates and places it will be easier to piece it together and find where these 3 trees join.
As your dad's dad is the unknown, then building the 3 trees for persons 1,2 and 3 will hopefully show the connection somewhere and thus lead you to find the parents of the unknown dad's dad.
Hope this makes sense, it will be easier if the matches have trees (but do check everything) or if you know the location. Also if the matches know whether you match them on their maternal or paternal line, as that will help narrow down the search and show you which branches you need to go back on.
I think you do have to draw up the trees of the matches, then your dad will fit in somewhere.
hth
Lisa