Tile – Installing tile over hardiboard

Assuming you do not have access from below, (if you do we have a completely different solution) you need to drill holes in the perpendicular grout line apx 16 inches from the parallel wall to the joists to start with. You may have to drill a couple of holes until you find a joist. Then calculate every 16 inches on center and drive screws. When driving the screws, they should bite and countersink themselves if you have hit a joist. Since you will have to re-grout the seam anyway, strip the grout and find the joists. Even doing this, I am not totally convinced a few screws will solve your problem. The best solution will be securing the subfloors from the bottom.

I regularly use Ditra. You can reuse it if you can get the corners down flat and co-planar.

Its not necessary to remove the old thinset, if it's well adhered. A new coat of thinset will bond to the old. A coat of concrete admix or bonding liquid (latex) the day before, will ensure old and new will adhere.

Schluter doesn't recommend using latex modified thinsets over Ditra and under porcelain tile. This is due to Ditra being impervious, porcelain being impervious and latex modified needing to 'dry'. Straight Portland cement thinset will chemically cure faster. If you have small format tiles (4x4 or smaller), you can use modified.

Ditra, in addition to being a water/vapor barrier, is an excellent crack isolation membrane. If you are using natural stone tiles or large format tiles (> 12x12), you should consider filling the whole power room area with Ditra.