If Parent Page > First Child, If Child > Show Next Child

I’d like to set up a navigation at the bottom of each page.

If it’s a parent page > link to first child.
If it’s a child page > show next child.
If it’s the last child page > only show previous.

Same for previous:

If first child page > link to parent.
If child page > link to previous child page.

Not sure how to accomplish this. I’ve tried hacking a few of the “previous/next” guides out there, but I can’t figure it out.