Your letter-writer is an @$$.
Still, you need that LOR. Unfortunately, you passed over a GOLDEN opportunity to have one less stressful part of your application. The whole point of a LOR is to have someone else verify that you actually have the strengths you listed. Now, you have the rare opportunity to eliminate the possibility that your boss won't do that. There's nothing unethical about it, since by signing the document, she agrees to all the opinions in the LOR - nowhere will it say that she actually wrote it. That's all you need.
So I'd go back to the boss, say you had a momentary lapse in judgement, and ask her to sign the rec letter that you have written. If she disagrees, hopefully you have someone else at work who has supervised you for something (better than a random co-worker) and you can persude them to sign the LOR you have written.