You put yourself in a worse position than the false accusation of your co-worker ever could have. She was wrong to falsely accuse you, but right about your needing an attitude adjustment.

You were given a reasonable assignment - train an employee - and complained about it.

You could have been 100% in the clear on the false allegation, but instead demonstrated poor judgement as well as a bad temper. You grilled everyone? Why? What good did it do you? Do you understand she would have had egg on her face if you'd left it alone?

In your response you can copy the original information that you submitted to contextualize your response. You need to ensure that the tone of what you write is very measured.

More than anything, though, you need to make sure that you figure out how to self-direct so that you don't damage yourself in your new job.