I don't remember any proposal in SII. I remember him losing his powers in the chamber and scenes with the phantom zone baddies doing their thing. The world wonders where Superman is, cue scene with them sleeping in bed.
Also that Man of Steel, Woman of Kleenex thing is kind of obnoxious. Maybe I just don't have a sense of humor when someone messes with the right of sympathetic characters to get it on without excess squick. I hereby wave the "suspension of disbelief" banner. <g>
But back to movie ranting: I honestly think its a huge faux pas for Lois to get the revelation out of that one scene when Jason pushes the piano. I concede that she should be suspisious, but to go and tell Superman explicitly that he's Jason's father because he pushed the piano...that's a big leap. I tend then to think that she's remembering SII's events. Some people wrote about this "deja vu" thing in the novel. That makes sense to me although I would think she'd be a bit more resistant (Lois: wow I slept with Superman and wound up pregnant. He must have erased my memory. Awesome!)
I don't think she'd use poor Richard. Probably, she thought the kid was his when they got together. Unlike someone who posted earlier I totally see her as the rebound type (especially considering that it's not like there was much of a relationship between her and Superman to begin with sans memories, if anything his departure seals for her how little he cared or something). Now she has quite a life for herself with a kid and a nice guy who'd be her husband in a heartbeat. It strikes me as least probable that she'd just shrug off Richard.
If Singer is really into unconventional families, I wouldn't hold my breath for an ending with our favorite couple. It would be keeping with the larger-than-life hero thing for things to continue as they are with Superman making frequent appearances in Jason's life as the kindly uncle from Krypton. Putting all that savior, you-are-not-part-of-them jazz is akin to shooting oneself in the foot when it comes to the very human complications we see.
That, or it's deliciously ironic. But that might be just me.