No offence, dude, but if she can't like you for who you are; not what you do, or what you have, then she isn't quite right for you.

I say let her go, ignore her, and go fishing again. You've made your apologies and explanations; now the metaphorical ball is in her court. She can either apologise for her (misguided due to lack of proof) accusations, or go take a long walk off a short pier, imo.

If seperation's what she wants, seperation and time to cool off is what she should get.