http://www.greenbuildingsupply.com/All-Products/Paints-Coatings-Caulks-Sealants-Adhesives/AFM-SafeCoat-3-in-1-Adhesive

Google is a wonderful tool.

tjdabomb,

Thank you! Unfortunately, I already contacted that manufacturer and they said they couldn't recommend their adhesive for this job. :(

I'd silicone 'em and forget about it.

Do you mean plain silicone? Can you recommend a brand?
That sounds like a good solution! Thanks.

That shower has seen better days. It may be time to demo and redo.

Well I'm just a homeowner, I would scrub out the area where things are missing, use a scrub brush or old toothbrush if you don't have scrub brush but you need a scrub brush since you are worried about your family's health, the mildew in the grout is not good for any of you especially if you have allergies, So fix the broken area by cleaning it out as good as you can, I'd use comet since it has bleach & maybe buy a mildew remover(smell strong) tho they are only good for about 1 time & basically they are bleach so might work better to use bleach & save your money, can pour a little bleach in small container & dip your brush in & scrub that area good, wipe out with old washcloth to remove all bleach or Comet(do not use together-chlorine gas can kill you) when area is clean & dry use a tube of bathroom caulk, comes in a soft tube,5.5 oz last time I bought it- cut the tip at angle & cover whole area & lay your pieces in way they should be & press down until even with the rest & way it used to be& wipe away excess caulk & clean off tile, leave it to dry for 24 hrs. This should take care of that problem but you should use the scrub brush & try to remove some more of the mildew, once off if you wipe down shower after using it it cuts the problem down greatly. I use Dap Kwik Seal, it at least can be removed if necessary as some ruin area around your tub or shower, becomes like plastic & no way to remove it but remove the tub or shower & start over DD had that mess. Good Luck & this should last until you move . Save rest with the tip cap on in case anything else becomes a problem, it will last a long time. So will cost about $5 or less to fix! If their are other areas where grout is out, fill it in. Be sure to use same color grout as is in there comes in white & almond & I think your grout is white but take a good look so you get the right color, it is not hard to do. Hard part is getting gunk out of that space as soap & mold will not allow the caulk to seal. Clean & dry area & it will work like a charm!! I know as I have done it for people.

Forgot to tell you to clean the tile pieces well so they will stick in the caulk!!

ya, plain old painters caulk would probably work too. I think my house is held together with only a few tubes!! :P