Okay, let's deal with humans first:

1) Is Taz is close to you whenever he bites the children? Or is he far away from your supervision?
2) When Taz bites, does he show fearful behavior (i.e. does he cower, does he hold his weight on his back legs, does his head shrink back, do the whites of his eyes show, does he avert his gaze)? Or does he tense up and posture (i.e. are his front legs holding the weight, are his muscles very tense and ready to "strike", is his chest out, are his eyes "hard" and staring)?
3) Normally, do you enforce NILIF or anything like NILIF? Or are things more lax and Taz generally gets what Taz wants? For example, when he wants attention, can he just climb into your lap or do you make him perform a behavior prior to it?

Usually, when small dogs bite around rambunctious children, it is a combination of fear and overarousal. Children are just awful at self-control So their energy, lack of control, and lack of better judgment make them easy targets for fearful small dogs. The best thing to do in fear-based cases is to teach child to respect the dog's space and to teach the dog that the child is a positive thing.

However, it sounds like Taz might have some guarding or possibly leadership issues if he bit in your lap and not before he was in your lap. If it were just this isolated incidence, I wouldn't say he's guarding, but you also note that he has issues with other dogs. It sounds like the dog-dog issues are based more on impulse control issues. It's very very common for dogs to be dog-friendly off-leash and not so on-leash. If the dog is *truly* dog friendly, then the Jekyll and Hyde behavior is usually deemed "leash reactivity": http://www.4pawsu.com/onleashaggression.htm

In all cases, there is hope. You just have to remember that, keep calm, manage situations well, and teach Taz appropriate behaviors. It can be done