Move mouse without changing mouse position

[grantmartin2002]

So I am currently having an issue where I need to move my mouse with AutoHotkey in some way other than simply changing the mouse position
https://youtu.be/NUASirrkNbI [Mod edit: Link fixed, again. Any new edit will break the link again.]
This video shows my issue. As you can see, at the start of the video my mouse position is already at the farthest right possible.
However, when I physically move my mouse to the right it still manipulates the application I'm trying to automate without changing the mouse position.
How can I achieve this functionality with AutoHotkey? Thanks.

Edit:
To clarify, the mouse position can change. I simply just need a way to move the mouse that isn't solely reliant on changing the mouse position. Any information/suggestions at all are greatly appreciated

[grantmartin2002]

Still having this issue btw.

[mikeyww]

One approach could be moving the mouse to the left edge of the screen when it reaches the right edge.