When I worked Home Health, I would pack bottled water in a small beverage cooler (like the ones people use to pack six packs in???) Those work quite well!
As for having to go potty? Well, I never would use a client's bathroom. Instead, I would make a pit stop at a fast food restaurant or gas station and go potty, wash my hands, take a swig of water, eat and keep truckin'!
Snacks to pack: zip-lock bag with dried fruit and nuts in it, the packaged peanut butter or cheese crackers, food bars, mints for the breath, string cheese (put it in the cooler with the bottled water), kid-lunch pacs (put one in the cooler with the bottled water), popcorn (never spoils), rice cakes, orange slices, peaches, tangerines, dried cereal.... If all else fails, stop by your nearest Krispy Kreme Doughnut shop like the policemen do, and chow down on some hot delicious doughnuts. Afterall, with all the running around Home Health Nurses do, one could use a "sugar high" sometimes.