If your hair needs it, go ahead with the trim. I know it sucks to lose length but think about how nice your ends will be.
As to getting her to only take off a certain amount, measure with your fingers as to what one inch looks like and show her on your hair.
As to getting it styled, on freshly cut hair, as long as the damage has been snipped away, one bout with the flat iron won't kill you. But then again, I don't know how much damage the rest of your hair has sustained, if any.
Good luck and let us know how it turns out!
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