Why didn't Quinn send Rembrant and Wade to their version of Earth in Exodus?

Short answer: Rembrandt knows breaking up the team is a bad idea, and that staying to help Exodus Prime is the right thing to do.

Long answer:

If you listen carefully to the dialog, Rembrandt says the following (emphasis mine):

Not if we take their Timer and go now.

Rembrandt doesn't get angry until Quinn and the Professor refuse to leave. He already realizes that either they all go, or none of them go. They've only survived many of their adventures by working together (and a lot of luck). Separating the group hurts all of their chances of survival. Wade would likely stay with Quinn and the Professor, meaning he'd be going alone, and therefore he's blaming them for missing the chance to go home.

Secondly, there's a more practical reason why they don't split up. Even though Quinn seems convinced he found Earth Prime, his evidence is somewhat circumstantial. It could simply be "very close to Earth Prime" like we've seen before.

Therefore, if Quinn is wrong, Rembrandt could end up stranded unless they send him with their Timer, endangering the original three even more - if something goes wrong with the Exodus plan.

Rembrandt also knows they should stay behind and help, even if it doesn't want to admit it. He's trying to balance his emotions of wanting to go home with doing the right thing. Even if he did abandon the others to go home, he probably wouldn't be able to deal with the guilt for very long and he's been shown to have a strong conscience over the past three years.