My horse would do that when I first got him, I just think it means she needs some more work with her manners. Don't let her into your space and after awhile she'll take the hint. After a couple weeks of ground work in the round pen & while grooming & leading my guy figured it out!
First, horses really respect proper spelling and grammar. If you don't believe me just try it for a year and see. Second, if she is pushing into you with her head then it means she wants you to move. I would not allow it and I would make her move so it became clear to her that I was not to be pushed around.
Umm... I do not agree with having the horse go backwards. What you want to be is like an electric fence. Have you ever seen a horse touch an electric fence after they know what it does? No. You want to set up 2 zones, a blue zone and a red zone. Say ur the red zone and you horse is the blue zone, you don't go into there space and don't let them come into theres. When you horse starts to swing his head around have your hand already up and if he comes into your space block him with you hand and lightly pop him on the nose or check. In reality you don't hit your horse is the face, never do that, but the horse is running into your hand, he is the one that made the decision. This will not make your horse head shy as you are not attacking him. I have tried doing the whole backing your horse up and then it can get bad... DO NOT TRY IT! I have had my horse become worse with that and you also don't respect his space. My horse has gotten so irritated with me she has reared. With the zones she stays in her space and I stay in mine and its all good, we both respect each other. With backing up they get scared. When you think about it when a horse came into the lead stallions area the stallion would just bit/kick the horse but they never chase them away, horses don't need long drawn out punishment but quick and too the point.
When my horse buys my feed it can have its own space but until then I own it. I can touch that horse at any time and can stand as close to the horse as I want to. The horse however can only stand as close to me as I want and can only touch me when I choose. Why?? Because the horse wieghs 1200lbs and can cause great pain simply by placing a well shod hoof on my big toe. The same is not true the other way around. I don't get carried away correcting a horse out of my space. I try to use the way they moved into my space as a guide to how much force to use to get them out of my space. If the horse just kind of drifted into my space I won't get too excited and just kind of wake them up and move them away but if a horse actively sought to push on me or step on me then I would actively seek to make them get the hell back where they belong. Not every scenario calls for a lot of force.
When you have been around enough different horses you will realize that to stay safe a horse must allow you anywhere around them but must stay as far away from you as you dictate. It's not a matter of domination or lack of mutual respect. It's a matter of staying safe.