For what it's worth, here's my response to her question.
Perhaps you need to start by asking what you want to accomplish. Are you trying to "convert" them to atheism? I suspect not. Are you trying to justify your position to them so that "they see the logic" in what you believe? It's unlikely you will have much success at that. It seems like the discussion degenerates into debates with each side trying to score points. Again, that is unlikely to change anyone's mind or reduce the conflict.
So what is it that you would like to have happen? Do you want mainly a good relationship with your parents? Then perhaps, as another person suggested, you simply respond to their arguments by saying "Thanks, I'll think about that" and move the discussion on. The other part of the answer may be to change the conversation and look for common ground. You can try talking to them about what is important to you - family, friends, helping each other, wanting a better world, etc. It's often a good idea to avoid talking about specific politicians in the process, since I suspect you will find strong disagreements there too. Instead, talk about ideas, plans, and what's important to you that they are likely to share and be interested in.
I'd be interested in hearing from anyone else who had similar problems with parents or relatives an how you handled it, and whether that worked out well or was a disaster.