Okay...suggestion for Episode 11.
Elladan and Elrohir bid farewell to Arwen (and Galadriel and Celeborn), and set off back for Rivendell. After they leave Lothlorien, they pass right by the Gate of Moria on their way to the pass on Caradhras [that the Fellowship tried to take]. While walking by, they discuss one of the old battles that happened there (burned dwarf reference?), and Elladan expresses the desire to go through Moria rather than around, since clearly there is still evil lurking within and it will be a good chance to kill some orcs. Elrohir is more alarmed by this suggestion and talks him out of it - references to Durin's Bane, and stories of people who enter Moria never returning. As both Gandalf and Aragorn will later enter Moria, it's not unheard of for someone to go through, but it is a foolhardy risk when there's no reason to. Perhaps the lingering suggestion of 'another time, then.'
This would set up Moria as an ominous place that the audience will expect to see again in the future. Elrohir could say something about who would want to go through that black pit if he didn't have to?!
We can't really have them go through Moria, as there's not enough time to build up the risk and resolve it in like 5 minutes of Frame Story, and this has little to do with Arwen. At the most, there could be a memory of something she said to them that flashes up during their debate about whether or not to enter Moria. She could be the reason neither of them want to throw their lives away recklessly. After all, someone hell-bent on fighting, with a vendetta against evil creatures and no wife or kids to worry about can do fool-hardy things. What's the harm in risking your life if there's no one who depends on you? The pain it would cause to those who love you can be a deterrent, so we could see that 'Don't make Arwen cry again!' is the motivation for not doing something stupid at this point in their lives.
Here is the map of the area, showing how Moria is definitely on the way back to Rivendell. We also know that the twins took the pass near Caradhras when they delivered the news of the Council of Elrond to Galadriel in Lothlorien, so it makes sense they would choose that route. Celebrían was ambushed in the High Pass near Rivendell.
In one rather memorable statement, Rich Mullins pointed out: "One of the great advantages of being single is you can still pick up hitchhikers. If you're married, you don't want to get, you know, slit or anything. Cause you got a family to support. If you're single and you die it doesn't really matter. So you're free to do anything you want to do. I love that!"
Substitute 'go looking for orcs' for 'picking up hitchhikers' and you get the idea.