Is the new dog being weird with new puppy aggression, or misguided affection?

Since you can't tell whether this is aggression (which it sounds like it might be) or not, I'd bring in a behaviorist (not an obedience trainer!) to watch the interactions for a while and tell you what you are dealing with. This may be something benign or easily fixed and nothing to be concerned about, or you may have a serious situation and need to rehome one of the two. I'd talk to your vet and see if they can recommend someone to come out and give you insight into which it is.