Ok you had a long post so I am going to try to offer some advice on a few of the things you hit on. First off your biggest problem is the horse is intimidating you. A horse is so sensitive and intuitive they can pick up on your butterflies so to speak...so this is the first thing you must do something about. Sending the horse off to the trainer isn't going to do much help to you, if it returns to your butterflies. Trainers are so confident they can handle even horrible horses and do well, where as a novice can't.
The horse in my opinion is just being a horse. They are like teenagers...they try you to see what boundaries you are going to restrict them too. Set the boundaries and inforce them. Even a dead broke horse will react to a new saddle that doesn't fit. Make sure your saddle fits the horse. If it does, then you need to make sure everything else fits, that there is no pinching going on. The head throwing is a sign of rejection. The horse is saying, NO I AM NOT DOING THIS, head throwing is often followed by rearing. Horses warn us, just like they do thier pasture buddies BEFORE they do stuff. A mare will swish her tale in frustration before she kicks, she will pin her ears before she bites...so she is throwing her head to warn you, she doesn't want to do what is asked and if you keep it up she is saying she is going to come up on you. We have a horse that had only been ridden with a hack so she had an issue with the bit and would throw the head alot because she didn't understand what was being asked of her. Make sure this is not the case here. Make sure you are asking her something she understands too, you have to converse with her. Make sure you are doing that correctly. I have seen people pull back on the reigns and kick or squeeze the horse to make it go. That is like pressing the gas pedal on a car and the brake at the same time. Make sure you are asking her to move correctly.
She is just asserting herself. Get yourself a riding crop or something you can carry in your hand to give you some confidence. I am not saying you have to ever use it, but it becomes your warning to the horse. Just like her head throwing, it is telling her you have some power. I am also going to suggest you buy an inexpensive rope halter that has some knots on the nose. Use this to correct the head throwing by putting on the bridle over it and attaching a lead line too the halter...walk alongside someone who is mounted on the horse...if she throws the head jerk down a few times on the halter...show her that her actions have reprocustions other than you just getting frustrated and getting off. She is learning every step of the way...right now she thinks she is in control because she has not been proven otherwise...again this is normal, typical horse behaviour.
Get focused. What do you want from your horse? What do you expect? Clear out your head...take a deep breath...and show this horse that is what you expect...and nothing less. Be more determined to get this horse acting correctly than this horse is at being disobendient and then the scales will start to tip in your favor. She will try you a few times, but if you are persistant she will knock it off. I am not going to lie to you, it will take inner strength to do it. Outer strength gets you not very far with horses, they are to powerful to conquer that way. It takes inner, persistant, strength. You must understand everytime you do battle with a horse and it wins, you are only reinforcing bad behaviour. So get in there with an all or nothing attitude. Do everything in baby steps...start small...disect everything into small chunks that you can achieve.
You said you had been adviced to lunge the horse. Ok, lunging can be used to warm a horse up get it flexing and its muscles warmed up for excercise. It can take the edge off of a horse that has pent up energy too, like one that is stalled alot, before riding. BUT it can also get a horse hot. Like my horse moves in slow motion until she is warmed up, then she is much more difficult to handle...so if you are having issues handling a horse that is "cold" getting it "hot" may not be so good before riding.
There are no perfect horses. Everyone has something that it needs to work on. And every horse lives by inbred rules. The main one is - I must lead or I must follow. She is leading right now, the same as any other horse you get will do, until you step up and say I AM THE BOSS you will follow me. They will all push you around if they get the chance.
I will close with this. Everyone needs to start out with a horse they feel comfortable with. Sometimes we get horses that we just don't feel comfortable with and it causes us to fear interacting with them instead of looking forward to it. You should enjoy your horse - point blank. This horse seems like it has some quirks, but nothing you can't handle if you put your mind to it...but that is your personal decision if you are willing to put the time and effort into it.