Making a very small photo big.

Just to support the idea that a higher resolution re-scan is needed: Looking closer, the examples posted are unusually blurry, blocky, and unreadable even for a small photo print. The picture below is a magnification of “8 26.jpg”, and it’s probably safe to assume that the actual original print shows more face detail than this, so it needs a better scan.

It also seems to have the blocky symptoms of too much JPEG compression, but that might just be in the JPEG copy that was posted here. Hopefully the original scan was not over-compressed like this.

However, it probably won’t benefit much from sending out for a drum scan. An old family picture like this often has too much inherent blur from a snapshot film camera with a cheap lens, no autofocus, and no image stabilization. So a common desktop scanner can probably resolve more detail than the print actually has. What a drum scan would help with is if the original was on slide film; then you might get more dynamic range from scanning the film.

@Chris B1969  I'd try find out what the maximum native resolution of the scanner is and scan to that, asking the scanner for more pixels is an interpolation and likely no better (maybe worse) that attempting to add resolution (upsize) in Photoshop. 

You might need a higher resolution scan, if this is important - maybe look for a drumscan service. 

I hope this helps
neil barstow, colourmanagement net - adobe forum volunteer - co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

<edit - nevermind>

In several of the screen shots, the width of the image is shown as 780 pixels wide. That is not very many pixels to work with, given that most computer and laptop displays are now thousands of pixels wide. An image 780 pixels wide doesn’t even cover half of most computer screens and TVs today.

In the screen shot 1open.png, the Properties panel shows that the uncropped Canvas size is 1583 x 2048 pixels. This is probably the number of pixels saved by the software running the scanner. 1583 x 2048 pixels is not a great start, given that you will be cropping the small photo out of that scan, which is why you are only left with 780 pixels wide.

A good approach would be to re-scan the print, but this time, in the original scanning software, set it to scan at a higher resolution so that the resulting scan has enough pixels for your intended usage. Also, see if it lets you select the area you want to scan, and if it does, select just the photo so that you are accurately measuring and scanning only the part you’re interested in, and not all that empty white space.

For example, if you ultimately want to be able to make a print 10 inches wide at 300 ppi,  then that tells you how many pixels wide the cropped scan needs to be: 10 inches times 300 ppi, or 3000 pixels. So when you go to re-scan that print, you tell the scanning software to scan just the snapshot area, at 3000 pixels wide (or 10 inches at 300 ppi, depending on how the scanning software lets you enter the numbers).