Sue
I agree with Nancy and would like to add one more thought. Old family photographs are a treasure and there is a vast store of information to help you when you work on them in Elements. An excellent book entitled Photoshop Restoration and Retouching by Katryn Eismann may be just the help you need. The book was written for the full Photoshop, but can easily be used with Elements as well.
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Sue,
Unless you already own full Photoshop, or want to part with about $650 US
to purchase it, Elements IS the "stronger" application.
The program provides all the tools you will need to produce professional
results, the skill level of the operator will be the determining factor for restoration success. However, even the most accomplished user can’t "make a silk purse out of a sow’s ear".
It is amazing what one can do in this program to improve old images.
I hope your Dad scanned the images at a real high resolution so that you
have lots of pixels to work with.
Maybe the images are printing out pixelated because they are currently set
at a resolution too low for quality printing. You would want your images to be between 200-300ppi for printing. Open one that you have printed and go to Image>Resize>Image Resize and see what resolution it was at.