You'll need to use the Track Matte to do this.
Just put the video you want to put inside the circle on Video 1 and a white circle on a black background on Video 2. Then apply the Track Matte to the video on Video 1 and, in its Applied Effects panel, set the Track Matte to define itself with the video on Video 2.
If you understand how the Track Matte works, it should be pretty simple. If not, you'll need to experiment with the Track Matte a bit or pick up a copy of my special effects book.
chiemgaubrownies and SG
Please be sure to indicate which version of Premiere Elements that you are using and on what operating system it is running.
In the suggested use of the Track Matte Key in all this, I do not see the requirement included for an outlined red circle. Track Matte, once practiced a few times is straight forward encough for most things, but for others not so, especially with certain manuvers. You do not have to use Track Matte for this. Below are two possibilities for your consideration:
If I used Track Matte
Video 4. Title 01 which is a white circle
Video 3. Video to which the Track Matte is applied and which uses Video 4 as the Matte.
Video 2. Title 02 which is a red circle which is larger than the white circle (how larger depends on the wanted size of the red outline.
Video 1. Color Matte which is white and obtained from New Item/Color Matte.
If I do not use Track Matte
Video 3. Title 01 which is a green circle.
Video 2. Title 02 which is a larger red circle (how larger depends on the wanted size of the red outline)
Video 3. Color Matte which is white and obtained from New Item/Color Matte.
Export that Timeline content to an appropriate file type consistent with your project goals. I opted to export to a DV.avi standard file.
Video 2. The DV.avi standard file to which I applied the Chroma Key effect to remove the green which is being surrounded by the red outline. Edit Effects to refine the effect.
Video 1. Video.
In moving things around with the mouse cursor in the monitor with several items, I find it is highly advisable first to right click the monitor, select Select, and then click on the name of the file that I want to move. Reminder, you do not have to use the Premiere Elements Titler to create the Track Matte. Alternatively Photoshop Elements might be used for that, exporting the png file from there into Premiere Elements.
Please review the above and let us know if any of that worked for you. I have road tested this a few times, but if a flaw got through, please do not hesitate to let me know.