It seems like a lot of resorts don't do much in the way of private lessons in terms of dialing the lesson to your needs beyond beginners. Often when I sign up for a lesson at the desk or over the phone I say I'm interested in working on this or that and on the advice of staff I've even specified can I get an instrucutor with a specific level of certification.
Then you show up at the meeting point, and there's somebody with a clipboard who might ask you a question or two, and then he looks over at a lineup of instructors and picks one. You have a chat with that person and then off you go, with mixed results. Of course if you find someone you mesh with you can request them going forward, but it's all pretty ad hoc.
I agree with Lamps - unless the resort you're working at is REALLY well known for their instructing (I don't think I've ever heard of one better than the other...) its a crap shoot.
I've worked as an instructor for a mid-sized resort in NH. The number one thing they told us was to help the clients have fun. Doesn't matter if they learn a little or learn a lot, as long as they have fun then "you have done your job." Seriously, I had a group of three or four eight year olds last winter and all they wanted to do was screw around and play in the snow. We probably did about 5 minutes of snowboarding for an hour lesson - the rest was snow balls and sliding around on the mounds of shoveled snow (our beginner area is near the parking lot). Of course, where you're working may have a different motto...
My advice? Find your niche. I found that I worked best with younger kids who were either JUST learning or had a small amount of experience. Probably ages 8 to 18. I couldn't do the older folks. Not sure why - maybe its because they already have pre-determined take on how a snowboard should be ridden, instructor be damned.
I'd be respectful and let your supervisor know what you prefer. You're probably not going to get that type of person every time around, but if you're in his/her they'll remember you when your ideal client comes along. Keep in mind that instructing is very seniority based. The instructors that have been their years are gonna get the "better" lessons. At least, this is what I've found.