My daughter was 13 months on our last trip and we didn't bring any sippy cups. Well, actually, we brought some of those take and toss cups but they stayed int eh luggage the whole trip. She just used the cups with a lid and straw that we got in the restaurants or food court. We threw them away when she was finished and never had to worry about cleaning them or carrying around smelly cups.
As far as diapers, I kept about 5 diapers in the diaper bag, plus an extra 1 or 2 in the stroller just in case my husband and I separated and the one with the baby didn't have the bag or something like that. For wipes I just took one of those big bags of Huggies wipes, with I think about 300 wipes in it, and then took a handful out of that bag, maybe 20 wipes or so, and put them in a Ziploc in the diaper bag. I'd check to make sure we had enough in there every morning and throw in a few more when needed.
For snacks we mostly took those Gerber Graduates Mini Fruits and Veggies, the freeze-dried kind. We'd also buy her a piece of fresh fruit every morning and hand that out when needed. Other than that we bought her snacks if she needed more.
Clothing-wise we always had a sweater in the diaper bag (trip was in April 18-29) and then usually a long sleeve/pants outfit. It usually got cooler at night, cool enough for pants, and we didn't always go back to the room mid-day to change.