You mean, you sit at the fence and try to line up horse to get on through the lead line?
I understand, you have it, however, “wrong direction.” What does that mean? Your mare is positioned to get on from the right side vs. typical left side?
That would not be so bad. It is good to be able to get on from both sides. I practice it regularly (from fence and otherwise).
If this is all it, then I would back off a little.
When I first started to line up horse to get on from fence, I already had following down to the science:
I taught him to move one step at a time forward, back, sideways from the ground. Later, I added just to shift his weight without moving. Like, you shape the body with almost only your thought.
He can almost become like a playdough. If he has a resistance, I just wait, change little something, and get him mellow again, then proceed. You want them soft in their head, because then, they become soft/pliable in body.
One trick: when backing the horse, tip his head slightly to the diagonal you are going to use. It makes it easier for them to understand, what you want. (to the left, if left diagonal, ie. left front-right hind)
This moving one step at a time is very, very important for the entire education of the horse. It makes any future training much easier.
I started by using my hands, one on the halter, the other somewhat pointing/touching the leg I had on my mind, and being really close to him.
Then, as he learnt to feel of me, I used dressage whip and repeated.
Then, I did it only with rope using the end to point, if needed.
I also added wrapping rope around him and shifting or even turning him that way.
Then, I got little off the ground, like a small stool and repeated.
Eventually, I sat on the fence with a rope and a long dressage whip. For first couple of sessions, I also experimented with longe whip, as it is really long and I could used it as a very long hand and reach across him to get him closer.
Sometimes, he got wiggly and I had to get off the fence, reshape him to the place I needed him and get back on! What made that part working was the fact that he knew his “stand” command. He would not move and, if he did, I would just reshape again and say “stand” again.
It was definitely a process.
I also gave him a treat, once he lined up and I got on. Not earlier! So, now, he lines up really nicely. 
I posted on the other thread that I mostly abandoned the western/natural horsemanship schools, but it does not mean I left them altogether.
This one piece of advice, meaning “one step at a time,” I have from “True Horsemanship Through Feel.” It is a great book and, even without in-hand background, the more you deal with horses and practice, the more you get out of it.
If I am way off, please, let me know. I will take it down.
Good Luck!
PS: You want to practice everything from both sides, but I am pretty sure, I don’t have to stress that.
