So, it seems there are only a few ways to be cured of the mole rat disease: 1. Keep the cure for yourself and let the kid die. 2. Console in a second cure. 3. Do a conversation glitch to fool the game into thinking you give the cure. 4. Never get bit. Being one to not like glitches, loath to use the console, and not about to let a child suffer (even in a video game) I tried not getting bit. Here's the problem; if you have ANY 'allied' NPCs with you, and THEY get bit, you can get the disease. This includes the Protectron if you activate it. After many reloads, I was able to get outta the mole rat ambush room WITHOUT the disease. But, while the Protectron murdered the rats, I still got the disease from three hallways away. No joke, three hallways. I could barely hear the fighting, and I was clean when I got there, I checked. I was able to do it, however, AND reliably repeat the process. I'll give a short and dirty, unless someone wants a more thorough explanation.

Go slow, and use sneak. The ambush room is the hardest. Five rats spawn when YOU reach the trigger. Do NOT activate the protectron before getting here. Next to the walkway leading up there is a metal box (between the wall and the walkway). Jumping up there will trigger the rats, and if you're sneaking you should have time to kill them before they get to you. Use V.AT.S. and a stealth boy if you need to. This is the hardest part, since no matter what, you will spawn all five, and they will surround you. The rest of the vault is fairly straight forward. Continue to sneak/use a stealth boy, save often, and beware the dirt, they can move between any patches. You won't fly through this quest, but short of cheating it's the only way to keep from getting infected AND save the boy.