My daughter and I have had fun creating Borax crystal formations by dissolving Borax in warm water, inserting a sponge medium then allowing evaporation to crystallize the Borax to the formation. However, both the glass vase and non-stick cooking pot that we used now have Borax crystals strongly adhered to the surface - to the point that they cannot be scraped away. So far, we have tried soaking in vinegar to no effect.
I'm hoping there's an obvious solution that we can apply to simply dissolve the formed Borax crystals.
Did you try boiling water to dissolve them?
Also I recommend doing your science experiments in containers that are of little / no value... don't use the expensive cookware.
What was the type of non stick cookware used? If it was teflon, I can't imagine the borax reacting with it so it should dissolve with water, low pH and heat in that order.
If it was a different type of non-stick cookware, it sounds like the borax may have complexed with the metals in the cookware forming an insoluble compound. If this was the case, the cookware is probably permanently damaged and the best you could do is grind the material off which would ruin the surface of the cookware but remove the borate complex.
I don't have a good home remedy, but base will be much more effective than acid in removing/dissolving borax crystals. In a lab/industrial setting I would would use an aqueous NaOH soln. I am not sure if an ammonia based solution will work as well. Soaking at least overnight.