I think this is a false dilemma, whether the dogs should get no punishment, or should be punished and taught their place. They need to be
taught. Positive training is generally much more effective (though I'll grant I used a can of pennies to teach Thor not to bark).
It is more difficult to train dogs if they aren't handled consistently... on the other hand, dogs do not generalize as much as humans. So they can learn that they can do whatever they want when they are with your Mom, but behave differently around you.
Also, if the dogs are super-hyper, that is a big sign they need more EXERCISE.
Finally - would it be possible for you to use more punctuation / paragraphs in your post? I had a really hard time reading it.