Brand new 3-way lamps not working correctly
Possibly - you're not screwing the bulb in tight enough. Most bulbs need to make one contact at the tip, these need to make two. 

But more likely these are duff fixtures.  "Better Homes &amp; Gardens" has never made a lamp in their long history publishing magazines; it's obvious they've "rented out their brand" (like Curtes Mathes of late).  A quick Googling shows that only Walmart sells it, so it's effectively a house brand of Walmart. 

Same with Allen Roth, it's a made-up house brand of Lowes.  

Those are the cheapest low-bidder units that Walmart and Lowes buyers can find in east Asia. For both companies, unit cost is everything and they drive a very hard bargain with their suppliers. There's a good chance they either came out of the same factory, or at least, the switches and sockets came from the same factory.  No wonder they failed the same. 



My brain short-circuited when you said you called GE and complained.  GE was founded by Thomas Edison himself and not only make jet engines, windmills and locomotives, they make the best ones on earth.  So let's talk about quality. 

In household and commercial lighting, I think GE is a smidge better than even the respectable top-shelf suppliers like Sylvania or Philips/Advance.  Cree is an American company whose thing is making LED emitters, and they're considered the best in that field.  Whether that translates into making good consumer products, I don't know.  Ikea has been better than I'd expect. 

Utilitech, Lights of America and Feit Electric, however, are the bottom shelf, the junk of the junk, they'll cut any corner to hit the price-point that'll make you put it in your cart.  That is why those brands are wall-to-wall at Lowes, Home Depot, Costco, Kmart and Walmart.  (notice I didn't say Target.)  And those stores "hold their feet to the fire" to make them shave cost... which is death to an LED, as I'll explain below. 

If you want to buy junk, that's fine, just do it with eyes wide open.  The big-box stores don't care - they've run the numbers, they know most people don't return bad product if it's cheap, and for the few that do, they make such good margin that they can afford it. 



Lastly CFLs.  I worked for the company that invented them, and they're rewiring their own buildings with LEDs.  That says it all.  LED is superior in every way, and at this point there is no reason to buy another CFL, ever. CFLs are gone from Ikea, get very little shelf space in CostCo, price is in free-fall (doing what electronics prices do), so in another year or two, CFLs will be relegated to the dollar-store, and then, gone.  Given the annoyance of recycling them and the nightmare of dealing with a broken CFL... and their short service life... good riddance.   Please don't buy anymore... it's time for that technology to go. 

Just for reference, LEDs have no toxic hazards and can be thrown in the trash.

Quality CFLs lasted 10 years.  (cheap ones didn't obviously.)  Given the nature of LED tech, I fully expect a quality unit to last 30-40.  Years.  Seriously.  But that rather depends on the quality of the build.  The weak link is the electronic driver circuit, and there are lots of ways to cheap those out with 1-year or 3-year components.  And that's what the junk brands are doing when the big-box stores put the price squeeze on them.