She is nervous and reactive because she needs leadership from you. So moving her feet, lunging her with lots of changes of direction are exactly what you need to do. Don't think of it as pushing her away. Think of it as you are the alpha and show her you can control her feet. You will give her permission to be in your space and then you will push back out, by showing her your a worthy leader she will learn to respect you and trust you. Lunge her for a few circles no more then four stop her bring her to you rub her face, back her up send her the other way, repeat. Once she has a good draw start changing directions without bringing her in. Make being with a good place to be a place she gets to rest, gain her respect and the catching problem will go away. Do lots of desensitizing, throw the rope over her back, butt, hind legs, front legs, neck and head one part at a time. If she gets worried keep doing it until she stops moving her feet and relaxes. Horses learn from the release of pressure so if you stop while she is moving you just taught her to be afraid. Use you whip or whatever you use to rub on her teach her to not be afraid of you or your tools.
There are ways to catch a horse when they don't want to be caught, but you have to understand what your doing and why. It involves chasing them and making them move their feet, then retreating when you get their two eyes, and making them uncomfortable for not looking at you. If your in a large space it is much harder, and practically setting them up for failure. The smaller the space the better until they get to where they catch you. Above all else be safe.