Hi,
sorry that you have to deal with all this. This is really unfortunate, considering also that you are pregnant and you should be ideally focusing on your pregnancy and your other young child. The positive thing is that your AN is still very small, and you are asymptomatic. This most certainly means that you don't need to rush into anything.
Of course we are not medical professionals, but we do share our experiences. So here is my experience: I had both my children before I knew about my AN. But for sure it was there during both pregnancies, because it was large when I was diagnosed, right after the birth of my son and based on the projected growth rates, it must have been quite large even when I had my daughter. I had both children delivered vaginally, breastfed both of them, and the pregnancies were entirely normal (no hint at all of what was about to follow ...). So for sure it can be done.
About the home birth, this is obviously something that you should discuss with your health care professional. Personally I would err on the safe side, to make sure that medical help is readily available if needed given the situation.
Regarding estrogen treatment etc., there is no real proof about anything. I didn't have any estrogen treatments etc., yet developed an AN. I have quite a few friends who had fertility treatments, but no AN.
Finally, as Jim said, SSD and facial paralysis are not guaranteed outcomes. I am SSD, but I don't have facial paralysis after GK and surgery. Given that your AN is so small, you most likely have the option of all treatment methods, some of which include hearing preservation approaches (such as middle fossa surgery, and radiation).
Marianna