How can I restore the waterproofing behind a shower/bath mixer/diverter?
At the very least you need to remove the two broken tiles and clean up the edges of the hole so that they are square.

Then, assuming that you don't want to remove any more of the existing wall your best bet would be to stick some batten to the edges of the hole from the back and then you can fix a new piece of waterproof platerboard to that. Seal the gaps and replace the tiles:



The battens don't have to be very big - they don't have to hold that much weight. The faceplate for the shower controls will help keep the new board in place too.

If you can, take the tiles off first and leave a border of plasterboard so that the join between pieces of board doesn't line up with the edges of the tiles. I know this will be difficult, but it will help ensure that the join is water proof.