I want advice on what to do here: I've been providing framed prints of my landscape photography to the hospital where I am employed as a nurse. I have done about 36 so far over the past 3 years. All have been the same size: 24"X36" black and white prints on Hahnemühle Photo Rag® Ultra Smooth 305 g matte paper, 4-ply white cotton rag mats, 3½" wide on the top and sides, 5" on the bottom, acid free Foam Cor backing, 1½" flat face black frames, 1⅜" deep, .118" non-glare acrylic glazing, a dust cover and security hardware. I charge $526 plus $20 to hang them. A week ago, they asked for some proofs to choose 3 from. I provided them (50) 9"X12" prints on metallic paper (to better represent the affect of glazing) to choose from. They came back with a request for bulk pricing for 8 with the above dimensions. Since they have been good to me, I took off $100 and the $26 for each of the 8. They agreed and I asked for them to tell me which ones they want. Two days later, (today) they are now asking for a price for just the 8 prints and they want to buy all of the 9X12" proofs. I don't like that. I priced my work on pretty much the high end of what multiple framing sites would charge for everything but the print. I never calculated the print's worth, but it sounds like they want to get them framed cheaper somewhere else. And as far as the proofs go, I have no idea what they want those for. I think I want to refuse to sell them the big prints unframed and if they want the proofs, I want to frame those too.
Any advice on how to handle this without affecting my reputation?

It sounds like you are offering a top-quality product. Have you explained to the buyer how an investment in archival prints and matting will hold its value for many years to come? Tell him you could use lower-grade papers and matting but in 10 years the prints could fade and the mats turn yellow around the edges. Explain that your reputation as a photographer would be diminished if the prints didn't hold up so you would prefer to continue providing the products you are currently selling. As for selling the portfolio prints I can't offer much advice. It may be some of the staff want a smaller print to put in their office rather than exhibit in a public area. You might ask them how they intend to use the smaller prints. This would be a reasonable request for an unframed print since they may want to match frames already in use in their office.

One of the many hats that I wore in the business was sales training and I reminded all of the trainees that we are ALL customers and those we want to sell to are no different than us.

People buy for THEIR reasons, not yours. It is also a buyer's market and unless you have an exclusive product, the buyer will always have other choices. Perhaps think about this: A picture of a landscape is far different than that of a staged setting. Why...? Because you do not own or have any claim to the scenery, which many times may be public areas. Did you get a release from the owner of the property you photographed to sell the image of their property for your financial gain? I suspect not.