Problem With Making Full Size Prints From a Scanned Photo

You can't put a price on family memories!  (Although I guess the photo lab can.  😉)  I'm glad it worked out for you.

I know I said in my original post that you can't fit a square peg into a round hole. But you can squish a rectangular peg into a frame with a different dimension.  However, this is probably not what you would want to do.  In order to crop out the ceiling and upper wall from your original photo, you can change the size of the edited, cropped document.  Go to the Image>Resize>Image Size menu. 

In order to fit the image into a 10x8 frame, check only the Resample Image box at the bottom of the dialog.  Then change the Document Size dimensions to 10x8 inches and the resolution to 300 pixels/inch:

This may make the people in the photo happy because it will make them thinner. (Depending on the change in dimensions, it could also make them wider.)  But, it really distorts the image:

So, in order to create an undistorted photo, you just have to use the crop tool.  You haven't said which version of Elements you are using.  There have been a few changes in the more recent versions, but they still work in basically the same way.  See the images in my earlier post for what you should see in Elements 2020.

There is a dropdown menu with choices to set the crop tool to both 8x10 and 6x4.  Set the dimensions for the particular size you want, then click and drag out a marquee rectangle around the image.   This marquee will display the area that will be cropped.  As shown in my earlier images, in order to keep all of the people in the image, both these sizes will still show much of the ceiling from the original photo.  You can change the crop area by redrawing the marquee or by click and dragging the "handles" at the corners and middle of the sides of the marquis area.  Once you are satisfied, click the green check mark to confirm the crop.

In the photos you have uploaded, the original only fills a portion of the scan.  The scan has an approximate aspect ratio of 12 to 7.2.  You said in your original post that the edited copy had not been cropped.  The edited photo you uploaded has been cropped from the original and the aspect ratio is nowhere near what will fill a 4x6 or 8x10 copy. 

In order to get an 8x10 image that will fill the photo frame, you will lose some of the original at the sides:

A 4x6 crop of the original will lose very little of the original image.

Does this help you, or do you need more information about how to crop the image?

You can't fit a square peg into a round hole.  A 12x8 photo cannot fit into a 10x8 frame (print) without some cropping or else some borders. 

The original is the same aspect ratio as a 4x6, so it should have fit, unless the printer failed to recognize the orientation of the image.  Were there large borders on top and bottom?