If you're going to give out a very complex emotional scene, you may do well to provide access to it early for your auditioning actors to prepare. I wouldn't go with anything too simple or you may end up casting someone who doesn't have the chops to handle the weighty emotional bits.
What I've done in the past is found about a page between the character being auditioned for and whomever they primarily interact with in the script. After initial casting decisions are made, I then would do callbacks if necessary to have multiple actors run those lines together to get a preview of their chemistry.
Initial audition was always just one actor and someone on the production team reading the other lines, subsequent auditions with multiple actors to find the best chemistry, and/or build an ensemble.
Also, if you give the actors something to work with in your audition room, that can be beneficial both for you and them. Whether you tell them to use it or not. (I'd suggest not, personally)
Granted this is slightly unfair and puts a bit of favor on people who audition well vs. people who are good actors but suck at auditioning, but by having a prop or something sitting there, you'll potentially get to see who the more creative actors you're auditioning are.
Similar situation was what led to my finding the best actor I've had the good fortune of working with on a few occasions,
Sasha Andreev. At the end of a long day of auditioning various actors for a short, Sasha strolls into the room. He was reading for the part of, well, basically an asshole (he's a really nice guy, yet somehow winds up playing assholes a lot.. lol).
The action in the scene was that his character was moving furniture around just prior to the start of dialog, and when the dialog kicks off he's very agitated. My director tells him to start whenever he's ready... Sasha reaches over and yanks this half banquet table off the floor holding it at a precarious angle, and begins the dialog. A few words later he drops it and continues on with the dialog.
We finish the read of that page or so, and everyone in the room erupts in laughter. The legs of table had broken off, Sasha had gotten our attention in a big way, and got the part. After sitting through countless auditions in that room that day, Sasha was the only actor who not only noticed that table was there, but actually used it.
