there are two things involved here - monitor and mouse... and i am suggest how can you fix if any of them is faulty.
For the dual monitors (which is more likely the issue), you need to check if their refresh rates and resolutions are synced... that's a very important thing but equally unnoticeable as well. Go to the Settings > Display > Advanced Display settings. Under the 'Refresh Rate' section, select the same frequency for both monitors. If that doesn't fixes it, try matching the display resolution as well.
For mouse (assuming that monitors are perfect), you should first check a few things like the polling rate, clicks per second, wireless connection band etc. The polling rate should be around 800 - 1000Hz normally and the wireless band needs to be 2.4GHz if you use a wireless mouse.
I hope with these two things, you can get your mouse work perfectly on both the monitors. Cheers!