L.,
I have a 2 yr old and we've traveled with her quite a bit. Contrary to what others have said, we have always brought her drinks through security with us, as long as they are in her sippy cups, its fine. You just have to take them out of your bag and set them in the bin. We just flew to Pittsburgh this weekend, and I had one sippy cup with 5 oz of milk, and one with 6 oz of juice, and I had no problem taking them through. Yes, bring a snack for her, if it's her favorite (like goldish are for mine) it will not only satisfy her tummy, it will soothe her if she's anxious. I usually bring coloring books and crayons, along with her favorite books. The magnadoodles are good also. If you have a laptop or portable dvd player the runs on batteries, bring a movie for her. I don't usually travel with the car seat. Cabs, and car services have them, you just have to request them. And definitely take the umbrella stroller. If your daughter won't sit in it, you can always use it to carry small bags (or a car seat if you decide to bring one). Also, encourage her to look out the window, and see "what animals the clouds make" - it's a fun game we play with my dd. Hope this helps and have a great trip!