I don't know the name of the tool, but it's used for removing oil filters from cars. That's what my grandma uses. It will get the lid off ANY jar, no matter how tight. Bugs me that I can't remember what it's called...
Our biggest problem is plastic Hellmann's Mayo jars. No matter how careful we are in resealing the jar after use, the lids seem to self-tighten in the fridge between uses to the point where even I have to make an effort to open the jar.
Try putting that big, foil covered seal inside the cap before you put the lid back on. Of course, now you'll have to wait until you buy a new jar.
Life is much more manageable when thought of as a scavenger hunt as opposed to a surprise party - Jimmy Buffett