Auto Insurance Claims: What can I do?, suprise suprise, ford explorer

Question
Hi there I have a 2 part question. I had my very first car accident on November 3rd and I am so frustrated with everything that happened. I was on a 2 lane road with my turn signal on waiting to take a left. There was a car coming in the opposite direction who was taking a right, and a ford explorer behind it who was at a stop waiting for it to go. The first car finally turned right and then the driver of the explorer motioned for me to go. As I turned, she gunned her engine and slammed into the side of my car. I had almost cleared the intersection so she only hit the rear tire on my passenger side. I got out to see if she was ok, she said she was and then we stayed on opposite sides of the road and waited for the police. When he showed up and asked us what has happened I gave my side of the story about how she motioned for me to go and the woman broke in and said "it was a miscommunication, i didn't wave you to go, i was on my cell phone and i was talking with my hands". The cop said there was nothing he could do, i aksed him if he wanted to write down on the report that she admitted to being on her cell phone and he said that there were no cell phone laws in florida so it didn't matter. Then he told me there were noinjuries so he wasn't going to file a report, I could go down to the police station and get the forms myself and send them in. He didn't ticket either one of us at the scene. So she left in her suv with scratches on the bumper and I had 6,000 worth of damage. I went to her insurance company first and suprise suprise they didn't want to cover me. Meanwhile she went to my insurance company and told them that she was driving 40 miles an hour (atleast) when she hit me and that she was never on her phone to begin with. So my insurance company didn't even try to recoup any losses. Oh and on top of all that she now 3 weeks after the fact went to her doctor and also has a PI to add to the bill. I realize that I did a stupid thing by taking a left infront of her. I know I didn't have the right of way, but I have been driving with no accidents and no speeding tickets for 9 years, I NEVER would have turned infront of her unless I absolutely thought it was safe to do so. Is there anything I can do about her being on her cell and waving her arms all around? I have no problem with 50% liability, but having it be 100% my fault just doesn't sit right with me.
Question #2 I had just moved to a new state when this happened and cancelled my old insurance on October 30th. I got a letter in the mail today saying that my old insurance was never cancelled, I am past due on my payments, I owe them 200 dollars, and they are sending notice to my bank that they will cancel me if they don't get it. So when I called the old insurance company they said that they can't cancel my insurance until they get my old liscense plates, which I sent them over a month ago. As I was on the phone with her she said "Oh wait they just arrived yesterday, Ill send them to the registry and when they get there, then we can cancel the insurance".
So when I told my coworkers this story they told me I could send the bill for 6,000 that my new insurance company paid to the old insurance company and make them send me a check for the damage.I technically still have coverage from them and they still want me to pay 200 dollars for something I tried to cancel months ago. Can I do that? It sounds an awful lot like insurance fraud to me. Could I have them reimburse me for the 500 deductible that I had to pay? I'm confused as I have never had to do any of this before.  

Answer
Hi Jessica,

WOW! You have a lot going on.

As for the accident, there is not much you can do. You did violate the others right of way. If you mistakenly thought she was waiving yo on but she actually was not, there's not much you can do.  Thats why they call them accidents.  As for your prior insurance. I belive if you send them a copy of your current policy showing the date the coverage went into effect, they should be able to cancel your old policy as of that date. Do not try to send them the repair bill. Since yo have already been paid for the damage, that would be considered insurance fraud.

I hope this helps
Richard Hixenbaugh