s far as possible I would try to eliminate the potential for damage. So go ahead and put a little fence around the tree, and if your Lab isn't able to deter your pup from aggravating the heck out of him, then put him inside or out of the way when this behavior starts.
If your little guy snaps or growls at you or your wife, then you need to get hold of him and tell him "NO" very firmly. But be calm, and keep your voice low, if you raise your voice or your emotional level, it will only 'wind him up' more.
At these times it would be good to keep a favorite chew toy in your pocket and offer him that as he runs past you to distract him from your pant legs.
Sometimes these moments of puppy craziness are worse in pups who are not able to be active during the day, and their energy just builds up.
If your pup is at home all day because you're at work, getting someone to take him out for a walk, or some playtime in the backyard at lunchtime may help. Even if you're at home, perhaps he's not getting enough exercise during the day.
Terriers are little 'action men' and need lots of stimulation and exercise.
Also, if he's being crate trained, make sure he has sturdy chew toys in his crate. Chewing is one of the ways that dogs release stress and it can actually help calm them down!
Once your pup is fully vaccinated I'd also recommend enrolling him at a local Dog Obedience School.
It helps to build and strengthen the relationship between dog and owner, the socialization experience is excellent for the puppy, and the energy expended by him will help to moderate his behavior. It's an all-around win.
I think in everything else you seem to be on the right track and are aware of what you need to be doing and how your pup is progressing.
I wouldn't worry too much about these 'puppy crazies' and don't think you need to be concerned about dominance either at this point.
I wish you the best of luck with this little guy.
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