Do people set up a single hand mode when using the mouse?

I sometimes need to use the mouse with my right hand. My left hand stays on the keyboard.

I have found that I often need to press some keys while using the mouse, such as enter. For keys on the left board, this is fine. But anything on the right board requires moving one of my hands there.

Is this a common situation? If so, are there examples of how people solve this? If not, can you point out my bad assumption?