Remove grout and reseal around bath tub

The grout between our tub and the tiled wall is cracked and we have had some mildew issues. We had the grout covered with silicon but it only made it worse and most of it has peeled off by now. The bath tub moves a lot when there is weight in it, so that makes it extra hard to seal effectively. We need someone to remove the grout and seal it properly with a sealant that can deal with the tub moving down when weight is in it.