Never ever normalize your recordings, a good limiter will produce a better result in terms of maximizing loudness. Drums can take a lot of compression and not suffer much in quality.
As for your snare problem, I think Audition has a Dynamics Compressor in it. Open it and try compressing the frequency range between about 700-1.2k to like a 5:1 ratio with a 3ms attack and 50ms release. I can't give exact measurements without looking at it, so use my numbers as a starting point. Lower the threshhold to just above your vocals level, and up the ratio until the snare sounds even in loudness with the vocals, otherwise you'll start compressing some of the vocal sound.
It's always tricky combating vocals with a band mix. If you have the resources, get a stereo submix of just the instruments and a separate mono submix of the dry vocal or a stereo submix if the house is using a stereo delay/reverb on the vox channel. This allows for the best tweaking once you get into a DAW.