u have 2 kids, and it's ur first time in china. I suggest package tour. is cheaper(our old folks made it possible) than if u go by urself and save the hassle of looking around.
I don't understand the rationale for the package tour.
If you have kids, just flag down a taxi, which are plentiful and cheap in any Chinese city. If you go to ulu places, you'll rent a car+driver or take a day tour, which also won't be an issue.
If your kids are not feeling well or if you are tired, you are free to start your day later instead of being forced to meet at the hotel lobby at 7am. You can come back to the hotel room earlier to rest, or change your plans during the trip. If the weather is bad, you can simply choose to visit a museum or other indoor attractions instead, and leave the outdoor attractions for another day.
If anything, I think free and easy is better if you have kids (not in all countries, but China is one of them). All you need is some research in advance, which you have to do too if you are taking package tour to find the best package.
The other problem with package tours is that you are so isolated from the country you visit that you actually do not become more familiar with it. You'll know nothing about the transportation options, hotels, people, etc.
So if you make a second trip, you'll find you know as little as you did the first time round, and based on the same reasoning, you'll be forced to take a package tour again.
I think trying to save some money by taking a package tour is false economy. You save a few hundred bucks, but you see and experience much less, not to mention the time you waste in duty free shops which translate into time and money wasted too.