is the iPod Touch less able to connect to Airport WDS wifi network repeaters than an iPad? Kindle also doesn't want to!
I've pretty much solved this problem. I do not FULLY understand why, but now I can have my iPod touch (and I am hoping my kindle) attach correctly to the satellite/repeater airport express.  Here is what I did:

I did two configuration changes to my central hub airport extreme router (i.e., the one that my other routers were merely configured to "extend.")  I realize now that these are both configurations that must be done at that central router, and the repeater routers then simply mimic or reflect accordingly.

-- First, I used the most recent Airport Utility (v6.0) and clicked on my main router (which, crucially, is an airport extreme that has dual band 802.11, both 2.4ghz and 5ghz.) 

-- In the airport utility, I clicked on that Extreme router and then in its funky popup window, clicked Edit.

-- Clicked the tab called Wireless.

-- Clicked on Wireless Options button.

-- the first config change I made on that page was to change the Radio Mode setting to "802.11a/n - 802.11 b/g."
     What nobody really tells you is that that hyphenated choice means that the 5GHz band will use the first of those two (namely, a and n, in other words the strong modern N standard will be used on this band ONLY) ... while the 2.4GHZ band will use only the second of those two, b/g, in other words, the devices that only can use that older weaker standard.
     So, it's kind of a segregation. I'm telling it "No, don't let the 2.4 ghz band try to handle traffic using N. That band will just take care of the old crappy clients." 

-- the second config change that I made on that page was to check the check box to make a totally separate wireless network name for the 5GHZ band.  Further segregating things.  When I tried my solution without this additional step, my problem did not fix itself, though I don't fully see why.

As I said, a few questions remain in my head, but the darn thing works, so I'm happy. Among many other questions... are those airport expresses dual-band too? I didn't think they were but somehow they are repeating this dual-band strategy?  Whatever. it works.

Wanted to say thanks to Richard, whose reply caused me to get off my butt and try more investigating into this.