I think it is possible to apologise to her without saying you are wrong. Balamsass and I do it all the time. One or the other of us says, "I'm sorry we had words" or "I'm sorry if I hurt your feelings" or "I should have been more tactful in the way I expressed myself" or "Can we agree to disagree?"
These kinds of statements convey you are trying to make peace. If the other person is loving, he/she will accept the gesture and move on.