IMO...what you stated implies that the converter is the problem.
Have you actually tried a USB mouse...on this system?
And, to satisfy my own curiosity, why use a USB converter on these two items...when the keyboard ports allow the devices to work routinely?
AFAIK, there is nothing gained by doing so...in fact, you wind up losing USB ports that could be used for other devices.
I have a USB mouse only because they are cheaper/better than the older PS2 mice. But converting a PS2 doesn't give anyone that advantage.
Wait to see what others say