Hi Sharon!
It sounds like you had some questions about the visibility of the picture-in-picture button when viewing a published Storyline 360 course. I'd be happy to help!
Testing this out on my end I viewed my published course with a PIP effect on both Chrome and Firefox.
The placement of the PIP button will depend on the browser being used to view the content. If both you and your learners are viewing the published course with Firefox, then the button will be displayed on the slide itself versus on the lower toolbar as with Chrome.
This article goes into a little more detail about picture-in-picture mode when viewing published content.
Please let me know if you have any more questions!