Wow! I can tell that there are not many people here on the Forum that have successfully dealt with a vicious horse. The only thing I find unusual is that it is a 2 year old filly and not a stud or an older mare. We have had a few vicious young mares come to us, but they are in a minority.
Let me point out the key things that happened that shaped her into the horse she has now become. I will try to 'debunk' some of the 'wrong' associations and responses.
First, let me repeat what I have said many times. I HATE WHIPS! I REALLY HATE THEM FOR ANY FORM OF DISCIPLINE!
It all started when I caught her the other day, and she was being really pushy and rammy on the ground just leading from the corral to the barn and in the barn as well. She would not let me physically push her or move her, so I dragged her to the roundpen and started roundpenning her to teach her that I can make her move and that she has to pay attention to me.
This was your first big mistake. This is what emboldened her and told her that she was in charge. Once you ask for something, you must make it happen!
Some horses are a lot more 'forgiving' than others. It is a quality that comes with a 'good, trainable disposition'. It is the main quality we breed for and the main reason we buy few prospects and raise our own at 20 to 30X the cost that we could purchase them for.
This... "misbehaving" is new, I've worked with her quite a few times before this, and she showed a little pushy-ness, but nothing out of the ordinary for a sassy 2 year old.
I suspect that what you are calling a little 'pushy-ness' and a 'sassy 2 year old', she has taken much more seriously. You should have taken it more seriously, too. The worst behavior you allow is the best behavior you have any right to expect.
Never, never, NEVER turn a horse loose that has threatened you physically. This can be anything from laying ears back and moving toward you, pawing at you, kicking at you, biting at you, etc. [I am not talking about 'nipping' but about biting -- mouth open, ears back and intending to hurt -- like a horse bites another horse it is trying to hurt.
If you ask a horse to back up --- which I consider the very best way to instill respect in a disrespectful horse --- make it happen.
There are two ways that I have found very effective to make a belligerent horse back up. Husband uses a third way. I will go through all of them.
One is to tie the horse up solidly to a good solid fence. Tie it rather long, four feet or so. Take a second lead-rope, stand off to one side, lead the horse forward until it hits the end of the tied rope, then ask the horse to back up along the fence. Start by just asking with a 'smooch' and a normal push / bump on the nose using the second lead-rope. If the horse 'bulls up' and refuses, step out to the side and start jerking the rope until the horse DOES back up. The tied rope keeps him from jumping on you or bulldozing over you. Be aware that a really mean one can still strike out at you. I've had it happen. You can stay out of the way and you can make a horse back up.
After a horse backs up, untie it and re-tie it somewhere else and do it again. Do this until the horse has an "I give up!" response. This is a relaxed horse, usually licking lips and always lowering the head. Then, do it out in the open. If all goes well, back the horse 15 or 20 feet and quit ONLY when the horse is willingly stepping back. Then, go tie the horse up for a while. I use NO petting or praising. I find this completely unnecessary and very distracting to the horse. I have had best results with using 'relief' and a 'lack of pressure' as the only reward. After the horse has been tied up for an hour or so, go over to it and see if the horse is still acting 'submissive' and cooperative. If it is, put the horse up. No feeding or petting or praising. Just put the horse away.
[Remember, that when you gave the horse 'relief and a lack of pressure' when you stopped asking her to back or move over and you put the horse out in the round pen, how quickly did she learn that she was in charge? It did not take petting and praising. It only took you taking the pressure off! This is how they learn!
The second way I teach a 'tough' horse to 'yield to pressure' is to take a piece of folded up baling wire and spank the horse's chest -- hard -- until the horse backs up. I also use this method to enforce a pushy horse to move its shoulder away from me when I 'smooch' and ask it to move. I just spank its shoulder. I do it quietly (nothing but a 'smooch') and I do it with as little movement as possible. I just want the horse to think it ran into a 'buzz-saw' or an electric fence when it did not back away from me when asked. I want it to think it was the worst decision of its life. Then, I quietly fold the baling wire up one more time, put it in my back pocket and act like nothing happened.
Third way: Husband still uses a chain over a horse's nose when it will not yield to pressure. I do not. I am not strong enough and having severe arthritis and degenerative joint disease since I was 40, I cannot win all of those battles, so I do not start them. It works for him. He is big enough to be effective on a lead-shank -- frequently with just a rope halter and a comfortable lead-rope, but always with a flat halter and a chain. I think I get a lot more done with a lot less fuss and noise. But then, I don't have Testosterone driving me to take a more aggressive route. [I'm glad he doesn't read this.]
Never, never, NEVER threaten a horse. Ask quietly and 'lightly'. Then demand with a little more force. If the horse does not respond correctly, make it think it was the HUGE mistake to not listen the very first time when you only asked nicely.
Always remember that it is MUCH more effective to back a horse up and 'push' it around than to make it run forward. I think they frequently see that as an 'escape' from the request.
Oh! And the horse jumping out of the round-pen? It was not from fear or confusion. She knew exactly what you wanted, did not want to do it, and jumping out was an escape. It is very common -- sometimes even with a rope on the horse. Just another example of why backing up is a lot more effective than running around forward. I've watched them jump out of 6' HD panels and try to jump 8'.