Hello my dear! Scary business, I know. Personally, I would not give the Gatorade. There is dye in it, plus other chemicals, that make it hard on the body. You could give water with sea salt - maybe 1/8 tsp per 16 ounces? I bet there's a dosage of that around here somewhere. And the GSE - you can do a few drops in a cup of diluted juice. See if you can find a probiotic - in a capsule - and break it open and sprinkle the powder on your little one's tongue.
Black tea is good for sipping in tsp amounts - easier on the system than plain water. Avoid anything with sugar in it! I'd only use the juice for getting other stuff down like the GSE, and then very diluted.
If food becomes an option - start with the BRAT diet - bananas, rice, applesauce and toast. (not all at once!)
There are some clever ladies here that could point you to better specifics. My main advice would be to stop the Gatorade (icky fake chemicals) and start the water with sea salt or black tea.
As far as spreading! If you can isolate your tot that is sick - one bathroom only - that might help. Wash wash wash your hands and hers. Throw out her toothbrush and depending upon where the other brushes are, either pitch them or clean them (you can use GSE for this, too!). Clean all your doorknobs and handles and surfaces with bleach.
It's so hard to keep it under control.