How to prepare a design document in Corel for UV printing on glass

I want to make a decorative glass panels on walls on our kitchen (the one between the hanging kitchen cabinets and the tabletop). The company I am negotiating right now uses UV coating as a printing method. I can't say for sure whether it's printing directly on glass or at the white glossy film glued to it.

Problem is, the image we're intending to print failed two coloring tests already. Red color becomes pink and the amount of colors drops considerably (details gets lost in the dark areas).

First coloring test was from CMYK image with color profile for US matter paper, saved to TIFF with ZIP compression.

Second coloring test was from RGB image (same CMYK as above but converted to screen sRGB) saved to JPEG level 9 baseline.

I don't even know whether they use CMYK color model or what because their "designer" don't understand my questions.

Is there anything I must account for when preparing the images for UV printing? Color profile, amount of colors, color mode?

The process is as follows: three separate raster images gets placed into the CorelDRAW layout and I assume this CorelDRAW layout gets printed directly to the printing device.

Will their CorelDRAW template (I can ask for it) help us in preparing the design which will not get colors screwed or it's a problem of the source raster image?

Will reducing the magenta color channel by some amount help? My main problem is red color becoming pink (I admit it was pink initially but it becomes much more pink in the resulting piece of glass).