[john70t]

Honestly, if the grout is that bad..there is not much to do but scrape off the surface and re-grout.

There is a flat square tool for cutting lines.
Use it slowly and lightly to not scratch up the tile.

You can get "Sand-able grout" in a tube.
$5-20 to do a shower.
Do one section at a time. L/R. U/D.
Put on tunes and submit to the tedious task.
Wipe the tile clean immediately after with a damp t-shirt or two. It dries hard.
Always be precise.

Caulk and use useless silicone grout sealant after a few days if necessary.

If the hot water supply is bad (i.e. my own rusty hot water heater) the problem will return in a year.
Need to flush that and replace the anodizing rod at a minimum.