It turned out that the "pink" tablet was actually the "orange" tablet. The "purple" tablet was actually "pink". So we added three tablespoons of vinegar to the orange container, which seemed to work quite well there. The pink tablet, though, stubbornly refused to dissolve. The egg that we put in there was taking on a very interesting mottled appearance. An even pink color, not so much.
So I said, "It looks like that dye doesn't do well in acid pH." Then I rummaged through a cabinet, didn't find what I was looking for, and called out to Gretchen, "Do we have any baking soda?"
It turned out that we did. And after carefully adding the baking soda a bit at a time to the vinegar solution until it stopped foaming, we found that the pill dissolved nicely and that the current and subsequent eggs came out a very reasonable shade of pink.
It's nice to find a use for seven years of chemistry training...