question: relax structure where upper, middle and lower move somewhat independently or connected? if you are connected, wouldn't moving your hips also moving everything else? in the same vein as your hand connect to your hara, and your hara moves wouldn't your hand moves as well? or am missing the point somewhere which is very likely?
i would add squatting up and down to make sure you don't brace the legs or circling the knees would work too or do both.
It's a good question. One that i'll take the long way to answer.
First, let's take a look at a body builder/weight lifter who's lifting weights to gain muscle in the biceps. You start with enough weight to do a set number of reps, a certain amount of time. You condition and build the biceps so that they can handle more and more weight. This is what I call localized muscle usage. You are actively training specific muscles to "resist" incoming force or weight.
At some point, from building localized muscle groups all over the body, you'll become "strong".
Back to your question about connectedness. In building a structured body, you want whole body connectedness, yes. But you want it in a "relaxed" manner. (I think this is very important for later stages of training in spirals.) In other words, yes, definitely, the hands are connected to the feet, the elbows to the knees, the shoulders to the waist/hip area. You want that connection to completely avoid localized muscle usage.
Think of the bones as very flexible water hoses in the body. Think of the push as water coming into the body through a hose that connects the right hand (where uke is pushing) all the way through the body to the left foot where it goes into the ground. Now, think of localized muscle usage as a tightening of the hose such that it closes it off.
You can hula hoop the waist without moving the shoulders or knees because your structure is relaxed, flexible, and yet strong. The push doesn't affect those other areas. Now, if you have localized muscle usage, it blocks the flow and causes pressure to build up in other areas. While you may be strong enough using localized muscle usage to withstand a push to your outstretched hand, you will not be able to hula hoop your hips because it will destabilize your whole body.
I wouldn't do squatting because it changes the vector of the push and you can still "cheat" to accomplish the exercise.
If you're using localized muscle groups, your sensitivity goes down. You aren't relaxed enough to "feel" changes in uke's movements or attacks. Your whole body speed goes down because you're actively tightening or loosening (basically) specific muscle groups which takes more time overall. Adjusting to changes becomes slower because of this, too.
If you use a relaxed, strong, whole body structure, your sensitivity to change sharpens. You can move under pressure or force because your body isn't locked or resisting that incoming weight or pressure. Your speed goes up because you're moving in a very connected internal manner.
Think of a sword to sword interaction if you can get the sword to be a part of your structured, connected body. Just as you can withstand the push, the attacker won't be able to muscle your sword out of the way, won't be able to off balance you, won't be able to move forward without putting himself in danger. Of course, getting the sword to be as one with your structured body is very hard.
But, hey, didn't someone famous say something about the sword is just part of your body?
Farther along in training, martial uses include being able to generate incredible power from minimal physical movements.