You are on the right track and your experience with your cat bears out my response to you and also my experience. The main point is not to be too attached to "rules" or which hand is best, but rather pay attention to whatever signals, information or message you get (remember: this is signal healing) and go with that. It may well be that it is better for you with one hand or another, and/or it may be better with a particular loved one to favor one hand over another.
The most important thing is not "the rules" or the "physics", but rather your love and intention. And to trust the messages you get in both giving and receiving.
You are doing great! Keep up the good work!