Please help me to figure this out. Born into a dysfunctional family, Marty1 alters his parents 1955 timeline. In this new, functional family timeline, Marty2 is born and raised until he disappears in his timeline's Delorean. Dysfunctional family timeline's Marty1 accomplished his mission and returned to Marty2's timeline, which left Marty2 nothing to alter in 1955(since Marty1 was already in 1955 doing the things shown the film), and as far as I can tell, Marty2 isn't represented in the rest of the trilogy. Did the film series leave a gaping plot hole, or am I just confused??
You are thinking in a more quantum theory like way. That is not how Time Travel works in Back to the Future. In BttF, there is always only one timeline. If someone alters the timeline, the old timeline simply is deleted.
Marty1 and Marty2 are not two separate persons. Marty1 is the same person as the "new" Marty2, except he was not altered (he still has Marty1s memories) because he was "out of time" when the timeline was altered.
So basically Marty1s history gets replaced by Marty2s history up to the point where he leaves for 1955. But they still are the same person.
There is something that needs 'fixing' (was going to write this as a comment, but it makes more sense as an answer) - George needs to stand up to Biff, which doesn't happen unless Marty gets involved.
If Marty doesn't get involved, Biff ends up dominating Georges life, which causes the dysfunctionality we see later on.
So Marty still needs to go back in time to ensure he has his father stand up to Biff in the car park, altering their future relationship.