If the mother feels she is getting good answers from the doctor, I think you can relax a little. If the mother doesn't, she can get another opinion. For example, you say you weren't told which bacteria showed up in the stool - which is okay if the mother was told and either didn't share it with you or didn't recall. But if the mother feels info is being withheld, that's not good. Of course, bacteria in the stool are completely normal, so it matters if it's a different bacteria or if the count is excessively high.
I'm not surprised that antibiotics are taking more than a day.I'm also not surprised that a child's demeanor would change when he's running a fever and having constant diarrhea. BRAT diet is standard but she needs to really push fluids. I'd stay away from things with red dye in them - no red drinks or popsicles unless it's plain red fruit in the popsicles and jello. I'd stay off yogurt and milk, but consider cheese to help bind him up. Hydrate hydrate hydrate all the time - he's losing a lot of fluids through diarrhea. I know yogurt can be helpful in terms of probiotics, but it's dairy is also a contributor to intestinal distress so I think it's a balancing act.
The leg pain is tough to evaluate - but a lot of flu-like infections make the muscles ache. He's also not getting a lot of nutrition if he's pooping it all out, so he probably feels weak and just generally lousy.
Not sure what the red eyes are - but if people have a bit of a cold and they rub their eyes after touching their nose and the mucus secretions, those germs can get into the membranes of the eyes and cause conjunctivitis. That's not serious but it's highly contagious. Or maybe the doctor felt it was something else - no way for us to know.
Serious hand washing needs to go on all the time or this will just keep recirculating. It's not something you want shared with others!
These things can go on for a while, especially with a toddler who may not have the most varied diet or be able to voice what's going on. If he's eating and drinking, and producing wet diapers in addition to all the diarrhea, and if he's resting a lot, this may resolve itself soon. I'd give the antibiotics more time to work.
If for any reason the mother feels that the doctor is not being vigilant or that she's getting the runaround, I'd look into another opinion. But 101/102 is not a life-threatening fever, and I thin you may need to give it a little more time.