Looking for an NI brass like Chris Botti's trumpet...

Try Symphony Essentials Brass Solo or Symphony Series Brass Solo... they are softer than anything else in the Kontakt library, but to get this tone you will have to reduce the attack, eq the resonance, and drown the freakin' thing in an IR 'verb.

I quickly got the Kontakt Factory Lib trumpet (orchestral) to get close to that tone, but there is no vibrato unless you want to really do minor wiggles on the pitch bend, or attach a controlled LFO to it inside Kontakt.

Good luck!