LNL - What about sending H a brief email so there can be no misunderstanding your position? Something along the lines of:
H - I'm sorry you think I am being a bitch because I don't care to meet you for lunch. I am willing to discuss any business you have with me via email. I am not trying to avoid any topics. It's just that I find our meetings seldom result in any positivity or kindness from you to me, and I am trying to surround myself with positive, kind people as I move forward with my life.
It has been my experience that ex-wives seldom have chatty lunches with their ex-husbands, so I don't really see why we should be any different in that regard. Since you have chosen to make me your ex-wife, why should you call me a bitch when I behave like an ex-wife? You have moved on, I am moving on, what is the point of meeting for lunch? I really think it is in the best interests of our daughter that we not stoop to name calling - a civil, polite working relationship is all I ask.