The detachments declare their countercharge at the end of the charge move subphase.
Definitely not. It's all laid out on page 283.
"When an enemy unit declares a charge against a regimental unit, and if that regimental unit does not flee as a charge reaction, each of its detachments that is within 3" if, not engaged in combat and not fleeing, can declare a supporting action. Any detachment that is able to make a supporting action may declare that it will make a supporting charge"
This is all happening in the charge declaration/charge reaction phase, as described on pages 119 and 120, before any models have been moved.
The moving does not happen until "The end of the Charge Move sub phase", but the declaration of the charge happens in the declare charges/charge reactions phase, just like counter charging would.
It should be obvious this has to be the case, because if the detachment didn't declare its action until after the enemy unit had moved, it would be literally impossible for a detachment to do the supporting fire/stand and shoot reaction.
The point is that wheeling to avoid the parent unit and the disordered charge won't get more models into base to base contact because the charging (7 cav) is wider than the being charged unit (5 infantry)
Wheeling to avoid the parent will most definitely get more models into base to base contact with the charge target than if they run into the parent unit on the way. If by wheeling the charger can avoid hitting some other unit, and instead make contact with the charge target, they
MUST do so.
You are absolutely not allowed to declare a charge against one unit, and then clip some other unit on the way in instead, if there is any way possible for you to avoid it. That's totally illegal and quite gamey. People would just use that to get around flee, stand and shoot, counter charge, etc. You can't do it. People could, for example, use it to get around detachments counter charging, as the phase for declaring charge reactions would be past.
This is explicitly spelled out on page 131
"If the charging unit is able to wheel to avoid the unit and complete its charge, it should.....if the charging unit makes accidental contact with an enemy unit that is not fleeing, simply treat the charging unit as having redirected its charge into that unit"
The scenario you are describing (hitting one unit in the charge and then somehow swinging to contact another unit and then ending up in a disordered charge) is not one permitted by the rules if there is any way to avoid it.
If there is no way to avoid it, the clause on page 130 "Multiple charge targets" spells out what to do. You have to declare a charge against both enemy targets, giving them both a charge reaction.
I have to say, playing the way you interpret the rules would make detachments VASTLY more powerful. But I'm afraid I don't think it's correct.