How to repair broken grout in shower tile?
It looks like the problem is not just the grout (which fills the gap between tiles) but also may be the tile adhesive is separating from the supporting structure (possibly plasterboard/drywall).

You can remove grout from between tiles using a variety of tools designed for this purpose. Then you can re-apply grout (and sealant if needed)

It seems likely that water has penetrated that structure, it might be best to open it up and assess what damage has been done and how the water got in.

In your case you may need to remove all the tiles, repair the supporting structure and re-tile. It's the only way to get the tiles to align neatly at the corners.