You can set different volume for different staves, even different voices on the same staff, so long as you route them to different MIDI channels in the Scoring Manager (and different instances of the "Piano" sound) in your VST.

This is gonna sound stupid but...how do you use the mixer in Aria? Whenever I try bringing it up in the score it doesn't seem to do much of anything.

The mixer in Aria is affected by dynamics sent to it by your Finale score (MIDI). If you want to set starting levels to try to balance instruments against each other (important since Aria instruments are not all sampled at the same volume an orchestra would give), you should use the Finale Mixer to set those base levels. Dynamics within Finale should do the rest.

In other words, I do not use the Aria Mixer for anything in Finale. I do, however, sometimes use the Controls and the Effects sections, and in Dorico one can use a version of the player to assign separate output channels to different faders in the Dorico Mixer, but that is not necessary in Finale.