The very first thing I mentioned about that video was that the man refused to stand up!
Remember to keep your expectations realistic. You have a very young puppy, and that dog was about 10 months old. That dog was playing, and seeking its boundaries. It was asking to be told what to do. The only answer the dog received was "Stop it, Cali, Stop it". All Cali understood about that was "Blah blah, Cali, Blah blah".
They are two very different scenarios, but I'm glad you mentioned the video as an example. Apply that behaviour to an 8 or 9 week old puppy, and that is typical puppy play. Your wife must use a strong, deep tone with the puppy when she means it. Your voice is naturally deep and louder. The puppy will learn that you two are on the same level in the "pack".
You both need to be consistent with the rules and routine, and try not to step in when the Jax won't listen to her. Let your wife sort it with Jax. She'll find her own way of letting Jax know that certain behaviours are unacceptable. I am surmising that you both have similar philosophies on "puppy rearing".
Jax will probably even be smart enough to learn how to coax treats from Mummy that Daddy may not necessarily give.
Jax will have it all figured out in no time!
Once the teething stage is completed, it does become easier as it is far less painful, for both of you. All the time they are teething, their gums hurt and they need to chew on things. Providing soothing chew toys helps a great deal. A dampened, twisted face cloth, frozen, provides soothing coolness to the gums and is reuseable.
Expect Jax to be this sort of silly until she is 12 weeks old. I'm sure you will start to see the changes in her by then. After that, it is 16 weeks, and then 20 weeks, and you're on your way.