When you walk directly in front of your partner (inside), she must lean directly forward, or toward where your feet touch the floor. When you walk outside to her R, she must lean slightly toward her R, or to where your feet touch the floor. If you walk outside to her L, she must lean slightly toward her L, or to where your feet touch the floor. She and you both should lean in the direction toward your partner's axis, i.e. where your partner's feet touch the floor.
Other than that, she just walks backwards.
Additional comment:
The description above only applies when the leader is standing on one foot, which he is often not doing. Better said that the follower should lean directly in the direction of the leaders axis.
Personally, I do not like this method of outside walking. Leaning sideways, even slightly, tends to disrupt most people's balance. Most of the time when leaders try/expect this with me (and with many followers I talk to) we feel that we are being pulled over.
I prefer a method that involves turning the shoulders to achieve the ability to walk "outside partner" (regardless of whether it is parallel or cross feet) and stay in milonguero chest to chest contact. By turning the shoulders, you can stay together and still get around the partner.
To walk to her right, turn towards her with YOUR right shoulder back. To walk to her left, do the opposite. Your shoulders have to be able to turn independently of your hips because your hips determine what direction you are going to walk. The tricky part is that many leaders will let their head turn with their shoulders rather than continue facing the direction they are walking. This makes the whole thing harder, and gives the follower the impression you are going to pivot her.
My opinion is that the advantage to using this method rather than the one suggested by AndaBien is that you aren't relying on the follower knowing a specific technique to "allow" you to execute the movement. If you are in flat on CE and you rotate your upper body, she has to rotate hers as well. If you keep your head looking down line of dance instead of allowing it to drift around with your shoulders, HER head will most likely also stay in a line with your line of dance rather than drift around when her shoulders turn. If you turn your shoulders and not your hips, she will more or less have to take the step in the direction you travel.
The only fly in the ointment is a slight tendency for the follower to take her step perpendicular to her shoulders. But if YOUR direction is clear, and you don't let your head drift with your shoulders, even if she allowed her hips to rotate with her chest, she'll have to go with you where you go
I can't emphasize enough how important it is for you to LOOK (with your whole head, not just your eyes) in the direction you plan to travel. Unless she is just so short that her skull is nowhere near yours, the position of her head helps her know where she is going to go when walking backwards. She may not even be aware that she derives some of her impetus for direction from this.
Edited to add:
Sorry... just watched your videos which came after AndaBien's post. Since the embrace in the videos is not flat-on CE, my method may not apply. This leader uses much more offset (the follower to his right) for outside walking than a flat on embrace calls for. He also uses a V sometimes.
The problem arises when a leader tried to use AndaBien's method while attempting to maintain a flat on (
directly in front) embrace to get the feet on different tracks. Since that's not what you are going for, then maybe his method is better for you. You will probably find however, that walking outside-partner to her left will be awkward with her shifted to YOUR right (or in a V) and a considerable shift of her position relative to you will be nessesary? Don't know... I'm not very good at following in a V embrace.