All tooth pastes contain glycerin -- even the non-fluoride brands from the health food store. Glycerin coats the teeth with a smooth (slimy) layer of.... glycerin (what else?) that will probably not wear off between brushings, even if you only brush once a day or less. Cavitations, which begin as small demineralized spots that your dentist can detect when his explorer "catches." This layer of glycerine prevents these spots from re-mineralizing, which is possible if they are addressed soon enough. Uny here makes a tooth powder that is claimed to help these spots re-mineralize. First made by Dr. Christopher, I think.
Anyway, hold off on that glycerine toothpaste until you find out more about it. Baking soda is better as well, but I don't think it helps re-mineralize.
Why do you suppose even the health food brands contain glycerine, if glycerine is so bad for your teeth? Could it be that people are so addicted to having that nice "clean" (read "slimy) feeling that they won't use anything that doesn't provide it.