Help with buttons and making them move around

Alright, here’s the dillema, and it’s largely due to complete stupidity on my part.

I made a button so that when I click on it, it moves from right to left.

The problem is, I want this buttom to move up and down while waiting for a click to happen so that it can move from right to left, while maintaining the same Y coordinate that it had when clicked on.

I’m wondering what is the best way to do this.

I thought of having an invisible line move up and down with the button to act as the path that it needs to follow, but that just sort of seems impractical. I’m planning to have many of these buttons at once.