I know dogs and children playing can worry some new pet owners. In addition caution for parents is to NEVER leave very young children left unattended with a puppy dog. If you trust your dog then you likely do not believe that the dog will attack. I would say the puppy dog is not much different than a small child itself. If a dog is unintentionally harmed or feels threatened it may bite.
For instance just as small children may push or scratch another child when they feel threatened. I would not subject your dog or child to possible harm by leaving them alone to play. For example always supervise dogs and children and you will be preventing a problem from occurring. I would say at first discourage your children from hugging and kissing their pet dog as most bites happen this way.
Most importantly regardless of the age of your children you should discourage roughhousing with the pet. I know some of the larger canine breeds can generally handle rougher play without becoming agitated. For instance large breeds may become irritated by ear pulling. I would say grabbing can accidentally harm your child. Besides large breeds may even knock over a small child unintentionally. Most importantly smaller breeds sometimes hurt children because they feel threatened.
I would say small breeds might not like overly affectionate mauling. In these cases they may bite or scratch in an effort to protect themselves. It is recommended that roughhousing should be discouraged with some pet canine breed. Besides you should seriously consider fully training any dog you choose as a family pet. In addition while some trainers may feel that the dog owner is adequately qualified to take on this task. I know dogs and children playing can worry some new puppy owners.