First, I would remove the grout. Use an ice pick, chisel, or dremel tool. its painstaking, but necessary.
Now, here is my feelings about grout around walls and floors. This is only my opinion.
GROUT IS NOT ELASTIC AT ALL. WHEN A WALL SLIGHTLY MOVES, THE GROUT BREAKS, IT DOES NOT GIVE.
I grout all walls and floors, but when I am waterproofing two meeting walls or one wall and a floor, I always use 100% silicon. It gives, its water proof, it comes in colors. it is more water tight than grout. Consider this if you will?
If you remove all the old stuff and get a nice smooth bead, you will not be messing with this problem for along time.