Is this color a pearl or metallic? If it is a solid color without pearl or metallic it can't "flip flop", it can have a case looking different from an angle but it isn't a "flip flop" that only happens with metallics or pearls.
"Panel painting" a door in the middle of a car is asking a lot but if it is a solid color they should be able to pull it off. A pearl or metallic, this is a BIG request.
The difference inside under lights or outside under sun light is understandable and hard to eliminate but not impossible. It's caused by a condition called "metamerism". You now how a color can change under certain light? You have seen this I'm sure. I remember we had some super yellow street lights in town on one street and my bright red truck would be absolutely hideous brown under them, this was caused by metamerism.
Color is being "killed" or neutralized by the light from the light source.
Ok, so you know this happens right? Well when you have two panels painted by a different paint company, you are going to have different formulas that created those colors. The different formulas will likely have different toners making up the color. Well the color may look the same under white light, but if the light is yellowed or blued as most every light isn't "white" those toners that are in the two "colors" (the new and the old paint) are being affected differently by the light because of the different colors within the color.
Whew, I think I confused myself with that one.
I have to tell you, it is the norm to blend, if the panels are prepared properly there is nothing wrong with it. I know I feel the same way as to not paint more of the car than what is really needed. I use to be a nut on that and would spend a LOT of time (too darn much time) matching colors so I could panel paint cars. But I have to tell you, if your car is a basecoat clearcoat, why worry about the fender and quarter having another coat of paint and clear on it? I know we don't WANT it to, as building up paint makes it more likely to chip easier. But man, if it's done properly it will hold up pretty well.
They "spotted it" right? THAT was blending. To "panel paint" the door in the side of a car is REALLY asking a lot. The hood, the decklid, you can get a way with murder. But a door in the middle of the car, that is a BIGGIE to pull off.
If they paint that door over and over because they can't pull of the color that is building up a bunch of paint and clear on that door too.
The thing is, can you find someone who CAN match the color for you, it's going to be a battle "forcing" someone who isn't capable (or they would have already done it) to match the color properly.