Two mouses interupt each other

Hello there!

I want to have a setup with a keyboard for mouse keys and a trackball for mouse movement. The issue is that when I try to hold mouse button (from keyboard) and move mouse (trackball), mouse button is getting unpressed. So I can't select text or drag-n-drop.

From what I understand, mouse movement events also go with button states, which are unpressed. This way? one device's mouse completely override another's.

Any suggestion of how to solve it?