[watwut]

Yes it is unethical, but she is unethical more.

Pragmatically, if she dates you while wearing that ring, chances are she will date another dude while wearing your ring.

If you need to stay on toxic relationship because of money, it is hard to leave, but not because you did not dated on the side. It is because you need to arrange living and job (or shelter). People in toxic relationships tend to be emotionally drained.