I am user a Atari ST computer and my original mouse has a very slow movements and little range for each movement, for this reason it is needed to move multiple times the mouse, I have tried to clean the ball and the inside of the mouse without improve the behavior.. Any suggestion to clean or to fix it?
On the other hand, I bought an adapter to include USB with PS2 protocol mouse but I do not know experiences about this adapter... Here the link: Atari mouse adapter
This is a common problem to retrocomputer mice. It is mainly due to the low dpi resolution of the sensors in the mouse. Each movement only translates to so many data points. Early mice like the one that would originally ship with STs are typically in the 75dpi range, later aftermarket ones usually top out at ~300dpi. You will see this same behaviour on other computers such as Amiga and early PC mice.
You may be able to set a "mouse speed" setting on your computer (I know you can on Amiga), but due to the limited dpi input, you quickly lose precision (it becomes more difficult to move the pointer by small amounts) unless you have upgraded to a higher dpi mouse, and even then it probably will not be as fast as you are used to on a modern computer.
Some later versions of the various retro operating systems (Amiga OS 2 or higher, later PC mouse drivers) will offer an "acceleration" feature which helps alleviate this by providing proportional movement instead of linear, where the faster you move the mouse, the further the pointer will move on the screen allowing you to improve responsiveness without sacrificing precision when you move the mouse slowly. You may be able to find similar 3rd party software to enable acceleration on your AtariST mouse if it doesn't support it in the version of the OS you have but I'm not familiar with that.
NOTE: The PS2 adapter you have, if its well designed will give you the benefit of higher DPI, making it analogous to later mice for your system, but you'll probably still want to enable mouse acceleration on your OS somehow for the reasons discussed above.
I can vouch for the USB mouse adapter. I have one myself along with this Microsoft mouse. It's 100% ST compatible, much more responsive than the official ST mouse and does away with the ball altogether (optical technology). Highly recommended.
If you want to stick with your original ST mouse, you can accelerate it using XCONTROL along with the MACCEL module.
