I downloaded the rear panel view of both your units. I know why you were getting the hum. You were connecting to the DIGITAL AUDIO OUT. That's for receivers with a digital audio decoder which your TV doesn't have.
Also, your combo DVD/VCR player is about to cause you a huge headache. You think your wife would hate learning to use the INPUT button? Wait until she has to figure out the SOURCE button on the DVD/VCR. Combo units are notoriously a PITA to use for the technically challenged.
Here's how it should be hooked up to (hopefully) accomplish what you want...
First, put away the s-video cable. You won't need it.
DirecTV box to DVD/VCR - Run from the Video and Audio R/L OUT on the DirecTV box (either 1 or 2, doesn't matter) to the Video and Audio R/L IN on the DVD/VCR. Should be easy as the connections on both ends should be color coded, Yellow for video, White for audio L, and Red for audio R.
DVD/VCR to the TV - Run the cables from the Video and Audio R/L OUT under the DVD/VCR side of the Magnavox's connections (the right side, the same side as the INPUT connections) to the Video and Audio R/L inputs labeled AV (GOOD) on the TV.
The above setup should allow you to do exactly what you proposed... being able to watch a DVD by simply putting it in the machine, then returning to DirecTV by simply ejecting the disk and turning the DVD/VCR off. (Hopefully, presuming the DVD/VCR will throughput the DirecTV signal when it's turned off.)
Now, if you want to set it up so can watch a DVD and want to get the absolute best possible picture, but still be able to switch it back to the above operation so your wife can use it, make this secondary hook up as well...
From the DVD/VCR run leads from the DVD side of the connections (the left side) using the COMPONENT VIDEO and AUDIO R/L ouputs. Connect them to the TV using the COMPONENT (BETTER) jacks. Take special care to make sure you get cables from the Y, Pb, and Pr connections matched. They can't be interchanged or Really Funky Things happen. I use a little trick with the 3-way video cables available most everywhere. They will likely have a yellow, red, and white boots on the cable. You can save confusion by attaching the yellow connector to Y, the red connector to Pr ("r" for red), and the white connector to Pb (it's the only cable left and has to go somewhere!). It's an easy way to keep yourself from being confused. The AUDIO R/L jacks are pretty obvious. Now you can deftly switch over to the COMPONENT input on the TV when you put in a DVD, but switch it back to AV and leave it there for ease of use by Mrs Warhorse.
One final note, if you have DirecTV's standard def service, the picture will be broadcast in standard (4:3) aspect ratio. That means it will be pillar-boxed on the screen (black bars on either side of the screen to take up the extra room that occurs when you put a square picture on a rectangular TV). For an extra fifteen a month you can get DirecTV's HD service with the integrated DVR. It's WAAAAYYYYY better. I recently made the upgrade when I got my flat screen and the difference is stunning.
Brad