Getting the old grout out is the worst. I bought a dremmel tool with a special attachment for removing grout. It takes a while, but it works. I’ve completely stopped using sanded grout ‘cause I’ve had several batches of it fail. I use the type of grout that already has the sealer included in the mix (I’m sorry, I’ve completely forgotten what it’s called)

We rented a special “grinder” tool from the tile store that did the trick much faster and better than our Dremel tool. We removed all of the cracked grout and vacuumed it out. Then we “shoved in” the new grout as best we could. Then we smoothed the joints, with our wet fingers, filling in the old joints and carrying the grout through and slightly over the existing grout. Then we washed the extra grout off of the tiles and let the grout set-up a bit. With the end of a toothbrush (the curved end, not the bristle end), I ran it along the whole grout line—both old and new. Let it dry a bit so that the grout has partially set. Then, using a wet sponge, rewash the tiles—trying not to disturb the new grout. If you should gouge out a bit of the new grout, simply re-do again.