What would you do if...(long sorry)

So I have this opportunity to work somewhere really cool with excellent hours, great bennies, and an increase in pay. I have been nursing for just under 2 years. I am pumped and excited and I have verbally accepted the offer which was extended to me the day after my interview.

Today I received in the mail a congratulatory (handwritten) letter and the application that I need to fill out. The 'official' letter will come after the application is in the recruiter's hands.

So in the application it asks for the name of your last several managers.

And there is a release form that says

I understand that the information and opinions concerning me disclosed to XXX and from XXX to (the new employer) may include both favorable and unfavorable material. I knowlingly and voluntarily release XXX and (the new employer) and their respective agents, and employees, from any and all claims and liabilities, including but not limited to claims for defamation, retaliation, discrimination, damages, costs and attorney fees, which have arisen or may arise in the future related to the information and opinions provided to XXX and from XXX to (the new employer)

So does this mean that they can ask for more than just employment verification, and does that mean that if a former employer and I did not see eye to eye and had a conflict, that the former employer can tell her side of it and I have no legal recourse if the job offer is rescinded?

So now I have this great new opportunity at another facility. I have verbally accepted and now am shaking in my boots that they will speak to the former manager about me and that she will say something negative about me. There was never a complaint about my clinical skills, in fact she even told me that she thinks I am a good nurse. But she also took the word of a coworker that I had said things and told other leaders, HR, and the manager of the floor to which I was all set to transfer to. All before talking to me, clarifying with me. (I was not allowed to go with her to the HR meeting about me that she had directly after calling me to the carpet. And I never received feedback, disciplinary action, or actually any comment from her again. I don't think she ever spoke to me again in the two weeks I was there before transferring, now I think of it.)

I am scared. I don't want to bring it up to the new place because what if she doesn't say anything? It was a number of months ago and maybe she is not so upset anymore. I know I am over it except for this issue now. Does that form that I quoted allow her to say anything she wants? Do I not have legal recourse if she blacklists me? Or can she just say 'yes she worked here from A - B'. Can I just say to the new place 'please contact HR to verify my employment dates' Can she tell the new employer the stuff she said she told the others? :uhoh3:Oh its a mess, isn't it? It feels like high school.

I am scared because I really want this new position at the other facility. And I have to tell my current supervisor that I have accepted the new job before they call her. What if they rescind the offer and then I have no job????

Any suggestions?