Out of the common pet rodents, hamsters are the most prone to bite. Many people will even tell you that they are nasty. I don't think so, but I do tell you that it's true that they are more prone to bite than any other rodent. If you have children, I suggest you get a syrian (teddy bear, golden, panda bear, black bear, ect. are all syrians, they just call them names according to their color and coat). Dwarf hamsters are smaller and more delicate for a young child to handle. Also, they are faster, which would make them more prone to accidents. Some people say that dwarves are more prone to bite than syrians, but in my experience, it all depends on how they are bred and raised. If you want a hammy less prone to bite, I suggest you get a hamster from a breeder, who handles the pups since they are young. That way, the hamsters will be more socialized when you get them, and will adjust more easily to you and your children.
You might also want to look into other rodents. Gerbils are far less prone to bite than hamsters, and are a lot more active. The only drawback, would be that they are way faster, so your kids would need to be more careful when handling them.
Last, your kids, if they are too young (and I assume they are by what you say), should always be supervised when handling the rodents, to make sure that thay don't mishandle or harm them accidentally. This will also protect them from bites, since a rodent can bite if it feels threatened. Good luck in finding a new pet!