That would be much easier to do using Premiere Pro because it supports nesting.

If you want to do it in Premiere Elements, it will be difficult to keyframe the movement of the videos and the background image so they move together.

In either case, you would have to create a background image with transparency where you want the videos to show through.  Photoshop or Photoshop Elements can do that.

That's a rather complicated effect involving Picture-in-Picture animations. It's certainly possible -- but I wouldn't recommend it unless you're fairly proficient with keyframing animations and creating PiP effects.

How proficient are you with these functions?