While it would certainly fix some things in the movie to A) have Richard go to the Dark Side (to mix metaphors), I'd hate to see it happen because he is a nice guy and a reasonably well-developed character as far as personality goes, and because that would really mess Jason up (see B) below). Background, outside interests are another story.
The hardest part to figure out, as far as "reality" and "justice" go, is this: if something - anything - happens to Richard but not to Jason, then Jason loses the only father he has ever known. That's just not a good thing for a little kid. Or B) does the little kid grow up to be a big bad villain because this twists him? Now THERE would be a twist in the Superman legend, but I'm not sure how many of us would enjoy the movie that results (Superman vs. the "other" Jason (not the one with the mask)).
Barring that, the believable options seem to be:
C) kill Richard - Jason grows up sad, but Superman gets to step in and take care of him w/o complications OTHER THAN Richard's parents (who weren't in SR) wondering about their grandson - they presumably would have been involved in his life thus far
D) kill Jason - then Richard & Superman can fight over Lois, or not, or Richard can just drift off sadly now that his supposed connection to Lois has been severed. Thing is, this would really scar our Man of Steel, and how would he get twisted?
E) kill Richard AND Jason - no Richard-Superman fight, no custody battle, but again - a sad Superman.
With any of the above scenarios, there's a good chance that Lois would blame Superman for her loss(es) - possibly damaging their relationship irreparably.
If we assume that we don't want our heroes/heroines/innocent kids scarred (this is Superman, after all, not Batman or X-Men) then we have to consider hokier yet well-established options to remedy the situation:
F) Dream sequence to explain away Richard, Jason, or both.
G) Mind-wipe on Richard, Jason, Lois, and/or everyone (except Superman?); reprint "Superman is dad" to fix it all.
H) Jason turns out to have some physical powers - sporadically or as he grows - but mostly mental ones. Have it turn out that when he was a tot, he was unusually wise for his age. He mentally pulled Richard into a relationship with his mom because he wanted, and needed, a dad and Richard was conveniently available and a good role model. Now that Jason has... other options... perhaps he'll release his hold. This could get pretty complicated and the motives would have to be well-established to avoid painting Jason as a creepy mind-controller.
I just can't think of a way to get Richard out of the picture without Jason ending up twisted and/or Richard being really hurt, and neither has done anything to merit such results. I don't know if there IS a way to resolve this w/o Richard and/or Jason becoming victims of one sort or another.
Hmmm, forgot the boring option...
I) Richard becomes a hero of some sort or another (mortal) superhero - he's close anyway - and he and Superman share custody of Jason. Richard, Superman, and Lois come to an understanding, nobody is scarred too badly, and it's just another modern blended family...
I am, of course, assuming we can't and won't kill off Lois - that would solve pretty much everything, as I could easily see Richard and Superman sharing Jason's care and upbringing once most of the jealousy issue was removed...