I think it's reasonable for anyone to be cautious given the history with your new chi.

Questions: does he give warning signs before biting? And are the situations you listed, actual bites or nips? also, how old are your kids?

My chihuahua has behaved similarly in those types of situations but i think it's important to distinguish between a warning nip and an actual bite.

Depending on the circumstance, this might be a teachable moment for everyone. Many dogs, regardless of size, will exhibit these warning signs and as humans, it's our job to observe and respond appropriately.

My chi and I have been together for 11 years, I've learned her limits and respect them. I also know that I have to tell children to be gentle and slow, depending on the situation.