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Hi Dave,
I wouldn’t worry too much about what you are seeing because it is best categorized as “play aggression”. It may look nasty, but young pups really like to “practice fight” and “practice hunt”. It looks like Lexi is happy to spar with him, and as you have witnessed with Lexi they tend to outgrow the extreme end of “play aggression” (some info in this article).
For sure I wouldn’t use any physical punishment such as skin pinching because he likely has a high fight drive and will just trigger the appropriate response for his temperament and can cause side effects of the pup expecting confrontation from you.
Does your pup have a dominant type temperament, yes, but that doesn’t mean he is dominant over you. As long as you control the resources and lead the interaction, you are on the right track. If he is playing and you feel Lexi has had enough and he isn’t respecting her signals, simply remove him from the interaction no different then any parent would remove a young sibling that was annoying an older one.
He likely has a lot of drive so I would print out a habitation chart and mark down anytime he is very “bratty” and see if we can find any trends. The next day beat him to the punch and schedule a good game of tug. He doesn’t know by default the best way to play with a human, so get a good rag or tug on a rope and play with him to wear him out and “play fight” with him by petting him and giving little slaps while is biting and otherwise keeping happy energy until he seems to be getting tired.
We can formally teach him to stop mouthing you if we feel confident that we are attending to the firecrackers need for some practice combat.
