sounds very similar to my second birth (husband, mom, friend). my first was a hospital birth. i chose UC for my second. MY mother, though, is *terrified* of birth. even animals birthing makes her nervous. the whole thing scares her.
when my mom found out my plans, she was definitely skittish at first, but the more i shared with her, not only about my reasons for my choice but all the information i was reading and all the interesting and empowering things i was learning, the more on board she became. she was still nervous and never truly totally comfortable with it, but she supported me and my decisions, and that's all that mattered to me. i wanted her to be there, and she was, nerves and all!
i was able to ignore her nervousness, though, because i knew despite her concerns, she loved me and trusted me to make the best decision for me and my family.
my advice? listen to everything your daughter has to say with a totally open mind, learn with her while she's learning, and trust that she's making the decision that best works for her and her family. it sounds like in your heart you do already, it's just your brain that won't shut off the 'what-ifs'. that's how my mom was. the best thing you can do is be there for her in whatever capacity she needs you to be. if there are specific concerns you have, certain complications you're concerned about, talk to your daughter about them and ask to read the information she's reading. in the end, you may not come to the same conclusions or level of comfort she's at, but you don't necessarily have to in order to be able to support her in her choice.