I don't understand this resampling stuff--why you are using it. When I need to make different size prints of the same photo, I do not do anything to the image but just specify the different print sizes in the software. Modern printer drivers are very good at dealing with this situation. I have never had any problem remotely like what you describe.
Not so sure that printers do a good job of resizing in pixels. If driver is set to 360ppi it expects 360, else it will resize to 360ppi. Not necessarily in a fine quality manner.
That is why f.i. Lightroom print allows you to set the ppi of the file to output to the printer.
Regardless of this, reduction in pixels leads to increasing contrast and hardness or harshness. In the example of the OP it is about x2 linear ,so x4 in total number of pixels.