I dance with what I call a flexible embrace.
What I mean is, sometimes I'll start out in a close embrace and open up so that We can express something musical, or some times I'll go the other way in order to better feel the connection. Sometimes my embrace will go from a "square" embrace where our shoulders are parallel to a "vee" shape where body to body connection is only on the closed side or rolls across the chest to allow Ocho's or back sacadas, leg wraps, gancho's etc...
I always think of the embrace as being elastic, that is to say, it may open up or change shape temporarily, or even break for short periods (as is the case for soltadas)but will eventually return to the shape it started from. The connection always remains and is paramount.
All that being said, the contact with the hands is always kept light and leading with the hands or pressure of any kind is to be avoided. The lead should always come from the core for linear movement or weight changes, and the torso for circular movement, and more often than not I will do both at the same time (leading a circular gyro while moving along the line of dance), this requires taking a back, front, side, or crossing step along the line of dance(to lead a movement with La Rhonda) while at the same time using disassociation of my hips from my shoulders to lead a circular movement of the follower around my axis. Any pressure from the hands (enough to push the follower off of her own axis) will make the dance very uncomfortable for the woman I am dancing with, and that equals a poor lead.
Rigidity leads to blocking or pressure, flexibility allows your partner freedom to maintain their own axis and freedom for self expression. If you are pushing someone around with your hands or a firm grip how could they possibly be having any fun.