So I'm trying to send a click of exact coordinates to an inactive program.
Why? There must be more to this than you''re telling us because frankly the whole exercise appears to be completely pointless. If you tell us what you're ultimately trying to achieve we might be able to make useful suggestions.

Your main problem is that you make no distinction between screen co-ordinates, the active client co-ordinates, and the inactive client co-ordinates, and more importantly which of the commands uses which of them. An inactive form is particularly tricky in that respect.