Garp DEFINITELY resembles Ace more than Luffy, both physically and narcoleptically. And of course, just about everyone has noticed a striking resemblence between Roger and Luffy.
Roger and Garp crossed paths in the past, an event that won Garp great notoriety and resepct for having "cornered" him (several times apparently!) But could it be possible these two are more connected than just a marine doing his duty of arresting a high-profile pirate?
A lot has been made of Ace being one of very few able to get the best of Luffy. Ace is also more of a follower (with his loyalty to Whitebeard) while Luffy is more independent, aspiring to be Pirate King himself. Could similar parallels be made between Garp (follower) and Roger (leader). Garp is also one of very few able to get the best of Roger - could they have been brothers?
That would make Roger a grand-uncle to Luffy, explaining the family resemblence.
Another theory by boiga in the 431 spoiler thread, is that Garp and Roger could be brother-in-laws. So their children would have married, making Roger Luffy/Ace's other grandfather, and Garp wouldn't carry the "D" title.
Educated guess: Garp's son and Roger's daughter (also a D) fell in love and got engaged. Roger, having made it around the world would have given anything to be there for his daughters wedding. During the wedding, garp will have found out that Roger is his son's father-in-law.
He'd tell roger that his daughter's life would be at risk from marine persecution unless roger turned himself in. They would tell the Marine HQ that garp had cornered roger.
Garp turns Roger in, leading to rogers death. Their progeny mate, leading to Ace and Luffy, who also have the will of D.
Personally I think this is the only decent explanation possible for a "Roger turns himself in" scenario.
It'd be poetic if they were family (through blood or marriage) and Garp turned out to be the one who led to Roger's arrest.