Well, I completely understand being irritated and angry. Her tone came across (to me) as rather pompous, and I can't stand the implication that homebirthers are all ignorant Luddites who haven't done due diligence and researched the matter thoroughly before coming to a conclusion. I don't think you need to kowtow to her or try to justify your decision to her or anyone else. You and your partner are adults, this is YOUR birth and YOU are doing it the way you want to.
That said, there's no reason to send her an angry email in response. Although the tone of the email was incredibly rude and condescending, in my opinion, it's possible--maybe even likely--that she wrote it out of love and concern for you and your baby. I would respond with something short and gracious, like
Thank you so much for taking the time to share your concerns with us regarding the impending birth of our child. Although we have weighed our options carefully and made our decision, we do appreciate hearing your perspective. We look forward to introducing our child to you after the birth!
Don't ever think you're not entitled to your feelings--you are! I would be angry too. But frankly, everyone is going to have an opinion about how you do EVERYTHING with your baby--birth is just the beginning. Get used to graciously blowing off unwanted advice.
Oh, and congrats!
good luck to you mama, and let us know what happened if you want to share.