Can I repair the grout on my bathroom, tiles are moving, is there a solution that is not striping the whole floor off again?

Sorry to say that the reason that they are moving is because they are loose and there could be several reasons for this - wrong adhesive, ply not screwed down or not sealed properly, if required. Unfortunately any repair to the grout would only cost you time and money for the same problem to happen again. You would have to find out why they have become loose so that when you re lay the new floor this does not happen again. I hope this helps. George.

if your tiles ae moving its not the grouts fault,the tiles are not bonded to the floor. you will have to lift the loose tiles and re-fix them then re-grout, regards Terry.

If your tiles are moving, there is no other option but to rip it all up and have it fitted properly. You need to start of with a good firm base, which by the sound of it, you havent got, plus using the right tile adhesive.

I'm afraid you will always be lifting and repairing tiles if they are loose, you could try some runny grout mixed with latex and let it almost harden before you wash it off, but it's a temporary fix. If the tiles are not bedded properly or surface under them is loose you will have to start over again