The Camera Raw plug-in when hosted by Elements does not have the Lens Corrections area where you can turn on CA reduction:
The Camera Raw plug-in when hosted by the full Photoshop or when using Lightroom, does have access to all the Lens Corrections parameters:
The camera raw plug-in in either Elements or Photoshop will respect whatever the Camera Raw defaults are for your camera so if you can get to that checkbox somehow and enable it and save it as enabled as the CR defaults then when you open raw files from that camera in Elements that default CA-correction on will be respected you just can't turn it on and off in the Elements/ACR UI.
You can also edit the Defaults file for your camera and change or add the following line:
Here is where that file resides on my computer:
And here is the context of that one line amongst some of the others in my text editor:
I am unsure if you'll need to add the line or if the line alread exists and you can just change the "0" to "1".
The filename on my computer is gibberish and will probably be different on your computer or may not exist if you've never saved customized Camera Raw defaults. You might try opening the Previous.xmp and changing the line in there, although I'm not exactly sure if that'll help or not.
Thanks so much ssprengel. I appreciate the time you took to respond.