Go, go, go
Kristen,
You should definitely go - it will be worth it. When I flew to Florida a couple weeks ago, I was so nervous that my 3 month old would cry the whole way that I was actually sweating. She didn't, and it was a learning experience. My sister flew back with us and she had her 3 and 1 year old children. The 3 year old had a backpack full of books, but my sister learned not to pack too much and expect them to roll their own backpacks because you end up with it as well as your own stuff. You be responsible for a bag that has books, crayons, snacks, and whatever. My sister had the double stroller and it worked like a charm. It was annoying to fold it and put it through the security belt, but it is amazing how much help strangers will give you. They will check it at the gate and it will be a lifesaver. You also have the benefit of boarding first since you are traveling with small children. If the kids are not behaving - so what - you don't know the people you are flying with and most have kids and sympathize for you. The trip will be worth while, the travel is such a short amount of time and will be a faded memory after you've arrived.