When I was fooling around with the console commands recently (I wanted to convince Captain Lonely-Gale that he was willing to marry my character), I went onto a marriage spree in frustration. Jarl Siddgeir can be married. I suppose that this would be the ideal way to get him out of Falkreath, because it was quite hilarious to make him cook me some meals and to let him set up a humble little shop in Riften. The only thing out of place were his clothes, but I guess I could fix that as well with some mod or with the console, if I'd be really motivated to have him as a husband.
I use to sleep in his bed when in Falkreath anyway, so
that part of the marriage wasn't such a big issue.

Yeah, anyway... I am not sure if he or his paranoid-delusional uncle are worse for Falkreath. Dengeir's neurosis reminds me too much of Skald the Elder's personality traits, and that one isn't really meant to rule as well.
Siddgeir is the better Jarl. Not because he's actually good at ruling, but because Nenya is. She's the real ruler of Falkreath, and manages to make sure everything's running okay in the Hold. If Dengeir takes over, his maid Tekla becomes the new steward. Not only is she inexperienced and unqualified but Dengeir doesn't trust her to being with, making her attempts to fulfill her duties for nothing. Furthermore, Dengeir's so paranoid, I wouldn't be surprised if people like Lod, his former bodyguard, either arrested or executed for being part of an "Imperial plot."
Long story short Siddgeir's an unqualified, lazy, rude, corrupt, arrogant jerk but has qualified people tending to his duties while on the other hand Dengeir is crazy, paranoid, untrusting, and probably dangerous, and has a woman he doesn't trust and doesn't know what she (or he for that matter, since he won't confide in her) is doing acting as steward, making their administration less effective.