How to see picture-in-picture button in my imove 10.1.10?

Drag your clip into the upper timeline, above the clip into which you want to insert it. Click on the upper clip to select it. That will cause the overlapping squares icon to appear in the toolbar at the upper right of your screen. That is the overlay icon. Click on it and select Picture in Picture from the selection box that appears.

— Rich

You are very welcome. :)

-- Rich