One thing to consider (and that I've been weighing myself) is that a gentle nip to the wrong part of the body can be quite serious.
When she was two, my youngest sat hard on our small dog and he turned around and gave her a gentle warning nip. Unfortunately, he caught her EYELID with his tooth. It broke the skin and honestly didn't look that bad, but because it was on her face we took her in to urgent care to see if she needed stitches (the same amount of force on an arm or leg wouldn't have broken the skin.) She ended up needing to be sedated to stitch up the little cut, and an opthamologist was called in for a consult to make sure that the tearduct wasn't damaged and they used dye in her eye to check for abrasions. It ended up being a really big deal (and crazy expensive.)
We consulted with an animal behaviorist through our local SPCA. In our case, they recommended keeping the dog separated from our young children (with gates, crating, etc.), gave us a number of training resources, and also said that they'd be more than willing to place him with another family without children -- I was afraid that he'd be totally unplaceable since he now had a "history of biting" but since it was clearly provoked (defending himself pretty gently when he was hurt) that wasn't an issue. We still have him and there have been no further incidences, but with another baby on the way we're revisiting the possibility of finding him another home. He's proven that he'll protect himself when hurt, not that he's aggressive, but protecting himself with his teeth is dangerous when little faces are so very close.
A behaviorist can help scrutinize the dogs behavior. It could be hierarchy, it could also be fear/insecurity on the part of the dog. Our consult through the SPCA was pretty affordable and I believe it was even considered a donation.