"How do we handle this?" the parents want to know. It partly depends on the age and training level of the puppy, but in general, you begin with management and progress to training. Thats to say, when the puppy is very young your best bet is to manage the situation. As puppy grows training will play more and more of a role until management is no longer an important part of the picture.
So what is management versus training? In the case of a puppy chasing, jumping on and biting at children who are playing wildly, management will start with the use of a crate. When the children are playing quietly they should be taught how to interact properly around the puppy, but all kids have those times where they are over-the-top with energy - this is a time to put the puppy in its crate, along with a stuffed Kong or a safe chew toy. Its just not fair to expect your children to change their behavior (they are truly being children after all), and its not fair to ask your puppy to ignore everything instinctual (running, chasing, tackling and biting that squealing human puppy).
As the puppy matures a little and gets some training, its time to move onto a new phase of management. Instead of crating your puppy when the kids are being wild, try putting the puppy on a leash and allowing them to watch, but not join in, the craziness. Try to keep your puppy busy with some easy obedience training (dont forget your treats and clicker), games or toys. If puppy finds it too frustrating then he or she may not be quite ready to move beyond quiet time in the crate.
Once your puppy can handle things on leash, the next step is allowing the puppy to remain loose while the children play, closely supervised by you. Use the time to practice some recalls (coming when called). Give lots of praise for every successful recall - thats a tough exercise! This is also a great opportunity to work on down-stay or "settle."
Keep things fun and positive, and remember, be sure to set your puppy up for success. These first few months are setting the stage for the behavior and relationship you get with your puppy over the next 12 or more years. Take the time to do it right and you will be rewarded many times over!