Ths answer is probably 'yes'. The yellow object behind Yang in that screen capture is not bright enough to be a sun.
Regarding the other 'shattered' moon, whatever happened must have happened recently as the debris field is not stable in that form, it would crash back into the main mass. So, the shattering occured recently and the debris is still drifting away (with inevitable huge meteorite strikes on the planet and chaotic disruption to weather, plate-tectonics and tides due to the change in the system's gravitational balances).
Apart from Ben-sama's explanation (thank you kindly), it also isn't impossible for a heavenly body to have two satellites. Although, granted, the RWBYverse('s home planet, whatever it's called) needs to have sufficient mass to keep those two moons, one whole and one fragmented, within its orbit.
... But then again, this isn't reality, so... *shrugs*
Yeah, we always forget that physics doesn't have to work in anime. It did just occur to me that the moon fragments are held there because they might really be not actual moon fragments, but that would just be too cheesy for me. Like the theory that the Nazis built bases on our moon.
Yang's moon just looks like a not-fully-risen sun to me.
yet its still completely dark out
Since this 'second moon' hasn't shown up at all in other speculations, it may not be anything at all. It could be either an unintential lightbox mistake, or it could be an intentional red herring so that RT members can laugh at everyone pulling their hair out trying to understand it.
If that was the case, I don't blame them. I would do the same thing.
I found a way to confirm that planet RWBY has two moons.
First to note, is that the fragmented moon appears in front of the Cliffside Altar during the intro.
Then let's move back a bit, in the Red trailer. Let's say Ruby went straight up until she reached the clearing where she did a little Beowolf genocide.
We now have the second moon, the yellow moon.
Geographically, the fragmented moon is in front of the Cliffside Altar, while the yellow moon is behind the cliffside altar.
Of course, this all relies on Ruby going straight on the Red Trailer. For all we know, she walked through the forest like it was a maze.
First to note, is that the fragmented moon appears in front of the Cliffside Altar during the intro.
Then let's move back a bit, in the Red trailer. Let's say Ruby went straight up until she reached the clearing where she did a little Beowolf genocide.
We now have the second moon, the yellow moon.
Geographically, the fragmented moon is in front of the Cliffside Altar, while the yellow moon is behind the cliffside altar.
Of course, this all relies on Ruby going straight on the Red Trailer. For all we know, she walked through the forest like it was a maze.
Nice catch. So now that the two moons have appeared in more than just the Yellow Trailer, I think we can assume that they are supposed to be there. On the other hand, I don't usually like citing the Red Trailer as evidence, because it's pretty out of character for the rest of the series so far.
This is the proof, IMHO at least, that the breakup of the White Moon occured during the time-period that is covered with the Trailers.