I'm in your exact position - I will have a toddler just turning 2 when the twins are born, but I also have a 4 year old that is severely allergic to peanuts so I always have an epi-pen and safe snacks for him. I didn't want a huge bag and I wanted it to be cute. I realize "huge" is a relative term, but I just ordered the Oi Oi Shopper. I liked it because it had 3 different ways to carry it - shoulder straps, straps built in to attach to stroller and a longer strap that could go across my body. I figure full, it will be heavy enough and if I need more, we'll have back up in the car, which we do even now anyway. And realistically, where am I going to be going with 4 kids by myself for any length of time, especially at the beginning! Good luck. I'm curious as to what you are doing about strollers, so if you want to e-mail me - feel free!
Mom to DS1 10.06, DS2 05.09, DD 05.11 and DS 05.11