Possible solutions:
A) click and drag the layout of monitor 2 a bit to the right until the left edge of monitor 2 is aligned with monitor 1, with the right edge of monitor 2 extending further past the edge of monitor 1. B) Find and use some software that gives you finer control over the arrangement of desktop icons (I personally love stardock Fences).
Explanation: my guess is that it's doing what you get at by mentioning the laptop resolution seems to be altered somehow. Maybe the resolution of monitor 1 is virtually extended to be as "wide" as monitor 2; so that Windows thinks the left edge of the desktop of monitor 1 extends to align with the left edge of the desktop of monitor 2.
With proposed solution A), I expect that then the icons of monitor 1 won't go "off" the screen to align to monitor 2, because there's not any virtual space further left to align to.
It's unfortunate if there's no built-in solution to Windows for this specific problem, or in other words that the only fix is to make sure the left edges of the desktops of vertically stacked monitors are aligned.