My family went through this same thing 2 years ago. I had a 3 yr. old and a 1 yr. old and we all got sick. Twice in one month and than again less than 2 months later.
First of all, the person who is the least sick should be in charge of cleaning EVERYTHING. Kitchen, Bathroom, Floors (if you have a crawler), Tub, Sinks... Than Lysol, Lysol, Lysol. EVERYTHING. Door knobs, telephones... anything you mouth or hands touch. Make sure you don't leave dirty dishes sitting in the sink and make sure you put your dishwasher on sanitize (if poss.) This bug can live in the air for a few hours and on surfaces a couple of days. It's awful. Whenever a child (or even you) throws up, make sure you have a box of rubber gloves (disposable) that you can use to clean it up so your hands don't come in contact with it. And, don't be afraid to throw away vomitted-on clothes. Or at least rinse them in cold water and than put them in the washer on hot. It's best to have clothes on your children that you don't mind putting in hot water to wash. That way you know the bug isn't still on them when they are supposedly "clean".
This bug is EXTREMELY contagious. Keep all healthy people away from the sick person and vice versa. We always quarenteen (sp?) our sicko on one couch and the other people can sit on the other, till it blows over.
Oh, and one more thing... If your doctor doesn't allow you to come in with a sick kid (contagious or not) than you need to find yourself a new doctor. My 1 yr. old was violently projectile vomiting the one time we were all sick and my ped. told me to come in immediately. I understand your doctor's reasoning, but that is very irresponsible to not see a sick patient just because they are contagious. Especially your 2 yr. old. They know signs of dehydration better than you do. That is awful. Find a new doctor... in my opinion or demand that you be seen. Don't be afraid to be a demanding parent. It's your responsibility to keep you kids as healthy as possible and that means finding a doctor who cares. If he is afraid of contagious children, he is in the wrong business and isn't up on the best ways to sanitize each exam room.
I hope this helps you feel more confident in deciding what to do the next time you have this. Oh, and since you have 2, chances are there WILL be a next time. It goes around and around if you don't clean properly the first time. Like I said, it can stay on surfaces up to 2 days and one little drop of fecal matter (diapers 2 yr. old or wiping improperly 6 yr. old) has a billion little buggies in it. Yes... I said, 1 BILLION. So, washing hands is a HUGE part of keeping this under control. Keep a can of lysol in reach and whenever you are vomiting or are going to bathroom (diarrhea), you should lysol everything right before you leave. Sink faucet, toilet handle and seat, door knob as you are leaving and don't forget the toilet paper dispenser. EVERYTHING. Lysol... it's great!