I love that video!
Yes, you are seeing the kind of ground skills your horse needs. Now you just need to learn how one gets there, step by step. The horse doesn't do all that so nicely, at first.
#1 is that your mare needs to see you as IMPORTANT. And that comes in how you handle her, how clear you are with your requests, and how firmly you back them up, and the 'bar' that you set for her, and how consisten you are with making sure she reaches that bar; every time.
I would suggest looking into Julie Goodnight's video series on ground manners. I find that she is a very clear trainer and good for beginners to learn the basics.
You are basically getting your horse to respect a feel that comes through the leadline, instead of YOU having to physically block or push your horse over or back.
For example, her going past your shoulder problem, or running you over . . . By the time your horse has passed you on the ground, it's too late. You should have addressed her intention to go past you when she was approaching the 'do not cross' line of your hand , held out to the side holding the lead rope. That hand is both a guide to your horse (follow this), and a barrier. the minute his nose is up to the position of that hand, you vigorously back him up.
There are all kinds of ways to back a horse up. YOu can turn and face him, push into his chest with a sharp finger or stick, you can wiggle the lead rope, or swing the tail end at him. Or, you can drag backward on the line while pushing on teh chest.
I think the last one might be ok for a hrose that really is just learning what that backward pressure on teh leadline means, but for a horse that knows already, but is simply not paying attention to your authority, I do not like to be that close in to the horse.
Here's how I do it. . . I walk along with my guiding hand out. If the horse's nose gets up to that hand, I lean back with my upper body, start to wiggle the rope enough to get his attention, and start to step backward. I do NOT turn around to face him. If he doesnt' move, I accelerate the wiggle on the rope until it's really moving back, kind of slapping under his jaw and into his chest. Yes, he will raise his head and get upset. I don't care. The second he steps backward, I decelerate the wiggle. I then ask again, with a soft wiggle, and if he backs a step more, I stop asking, pause for a mintue to let him soak on that, then walk forward again.
Over time, the horse will be more attentive, and if he strays too close to my guiding hand, I only have to raise that hand, and maybe say, "Ah, Ah!", and he will pause, allowing me to step forward and put more space between us.
Julie Goodnights videos will show all this.