From the sounds of it the problem is MP is respecting the setting and both machines are flipping it.  So the first machine flips left to right and then the second machine flips it again as any input from Multiplicity is treated the same way as input from the local mouse.

So disabling the option on the secondary would remove the double flip.

Going forward we can investigate adding an option to MP to make it also flip it (so things get flipped three times) in order to handle this slightly unusual situation, though I cannot make any promises as to when such a feature will appear.

I guess it depends how you view it. Both machines are set for a left-handed mouse user. Multiplicity runs on both machines, so presumably it has access to the mouse settings on each machine. From a user perspective, I don't care how these settings are enabled, as long as the mouse works as expected.

You may consider it a slightly unusual situation, but I know a fair number of developers who use left-handed mouse settings, and it seems only reasonable that Multiplicity should allow secondary machines to be used according to their individual mouse settings, without changing the Control Panel settings every time it is used. I don't really see how this is problematic if it can read the mouse settings on each machine. 

Multiplicity isn't the first software product not to correctly support left-handed mouse settings (Carbon Copy, Checkpoint, and LogMeIn originally had this problem), but they were eventually fixed.