I'm thinking of letting my helper take the blame for something she didn't do
Why do you want to put the blame on your helper?
I hate her for doing things that are making my life more difficult
It's wrong to put the blame on someone who didn't do what you're accusing them of. If your helpful is making your life worse then fire her, don't lie.
If I fire her than my life will become much better.
If she is truly making things harder for you, then maybe she is not the best fit for the job. Just make sure that you are doing it in a fair and respectful way.