I don't want to go back to the same terrible dentist to fix the problem she created. She also did unnecessary work and charged for a full mouth cleaning on nine teeth. What can I do to get her to reimburse the fee I have to pay to another dentist?

Fix what problem?
What unnecessary work?
I take it another dentist told you this. It's one dentist's word against another, and we certainly can't judge, especially with not one detail.
So your choice is to sue in civil court, usually Small Claims. But you could easily lose without the testimony of the second dentist, who probably won't want to testify.
You can file a complaint to your state licensing board. It won't get you anything, just go on file.
Many of us have had less than satisfactory service from doctors and dentists. A lot of situations aren't worth a lawsuit. You decide what you need to do.

It's too complicated/lengthy to go into properly online. I had to go back to this dentist four times to work on nine teeth. That's not including the first initial visit. She said I needed a crown. The first crown she ordered she said came in cracked. She had to reorder it. I don't think she ever did reorder, because the crown she did put in is also cracked. The filling she used to put under the crown is now leaking out through the crack (hole) in the crown. Plus there is a hollow spot between the crown and the tooth next to it that is just a cavity now. She put some sort of packing there that just flaked away. Now there's just this cavity there between the crown and another tooth. The work she did is deplorable. I didn't need another dentist to tell me the work she did is a total mess.
I never went in for an evaluation. I charted out on the form they give you what I wanted to have done. I don't have dental insurance and I told them that. I am 73 retired with a limited income. I was billed $1,206.00 for one crown and cleaning on nine teeth. She wouldn't allow the hygienist to clean between the two teeth where the problem was I wanted corrected. The hygienist told me she told her not to clean there. The condition I went in for is worse, plus she gave me a damaged crown.

I'm sorry I made it sound like you needed to go into detail here; I was just asking as a way to indicate that we couldn't assess. The rest of my reply still applies - small claims. The fee is about $50 depending on the state. I have no idea if you will win or lose. If she doesn't show up, you win by default (including the fee), but then you have to collect, and some people don't pay. Most courts allow for resolution by mail before going to court, so it's worth a shot. You can try the BBB and the licensing board.