Normally I wouldn't expect screen resolution to affect the coordinates of a given point within a window, provided that the window is of identical size, given that a pixel is a pixel, regardless of how many there are on screen.
Unless you're using different scaling settings for these different displays, and/or resizing the window.
If scaling is the issue, you'd need to attempt to work with percentages, by calculating the position relative to the window's size (E.G. using "{ACTIVEWINDOWWIDTH}" and "{ACTIVEWINDOWHEIGHT}")
If the window is actually resized, that may also apply, assuming the various UI elements you're trying to click remain visible and in the same relative position.
I understand from your previous posts that you have no choice but to use mouse movement, but unfortunately this type of thing is the reason why it's considered a last resort.
Mouse movement is intended to be used in a feedback loop where the user visually identifies the elements on screen, and adjusts the cursor position to suit, which is not well-suited to automation.