I agree that your mother has a right to her feelings, just the same as anyone. That said, I don't think she has a right to manipulate you or anyone with her feelings--and threatening to disown you is very much a manipulation. I also sense that it is not just fear for yours/baby's wellbeing that drives her reaction, and it is not just her sense of having been 'lied to'. It is her ego in overdrive; it is her fear of losing any sort of control over you. And, by making such a 'nonmedical' choice, you have (in her ego's opinion) 'attacked' her life's work and some beliefs she holds very dear (beliefs about the primacy and efficacy of modern medicine).
About the idea of 'lying' to her. I guess everyone's right....it WAS a lie of omission in the strictest sense; and it was ALSO not your obligation to share all the info with family about your birth plans. (Personally I think wanna-be UCers are fairly nuts to take on family dynamics and stress by giving advance notice about UC plans! Well, unless you have the most cool, accepting, etc, parents and extended fam in the whole universe
) An important part of the equation is the need for her to ask herself how she is creating a relationship with you that necessitates your lie of omission--and that is something very difficult for most people to consider (so much easier to point the finger of blame--'it's all YOUR FAULT, cuz YOU lied to me...' far harder to ask oneself 'how am I contributing to the necessity for my dd to hide things from me? What about me makes it hard for her to totally trust me?').
So, when it comes to the idea of 'apology', here are my thoughts--that you can express regret/compassion for her feelings, acknowledging that she feels betrayed by your lie of omission; but you don't have to feel bad about that lie at all.
My own mom is not a med professional, but she certainly is a 'maternal pro'--having raised 8 kids. And her ego was always similarly involved in her struggles against me and my crazy choices (non vax, fam bed, etc). In our case, I disowned her several years back, after some 20yrs of trying to come to terms with her, trying to change our relationship to a more positive and egalitarian one which she just was NOT going to have! It meant too much to her ego to a) have me make the same parenting choices she did, so she could have the self-affirmation inherent in my imitation of her and b) have me accept her 'authority' over me and my life....which, if she was honest, she would realize she never had in the first place! (I've never been anyone's obedient follower
) She simply could not imagine that we might have another, and satisfying, relationship of mutual respect and consideration.
In any event, with your birth you have stepped further into your own life and further away from being a child in need of mommy's approval and support. That is hard for many parents to accept...as I like to joke, when going through yet another round of stress with each of my kids as they have come into adulthood--'breaking up is hard to do!' (Hey, I'm a pretty cool parent--according to my kids--but even *I* have to go through a sometimes difficult letting-go process as kids become teens become adults and our relationships have to change. And well, they can be real bears when it comes to stepping free!). However much your mom might have thought that you guys had gotten through that already, however much it seemed that you guys had already shifted gears with your growing-up-and-leaving-mommy, this represents another (and in her mind, probably gigantic) step: another step for you into your own maturity and power, another step away from the original mother-daughter relationship. YOU feel euphoric about your UC, and it means so much to you, your marriage, your family....SHE only feels abandoned, betrayed, afraid, angry--because she can't yet imagine having a good, an even better, relationship with you on these new terms.
I agree with pps who've said--keep your heart open. Time will do it's job of healing hurts, and also of showing her that she would probably rather have a relationship with you and your kids than not. My mom is very much an exception! She never stopped waiting for me to toe her line, never could see how our conflict was just as much HER input as mine, never stopped finding ways to argue with me, no matter what I did or stopped doing (and even my sibs noted my efforts, and her refusal to do anything different; her own sibs warned her that she was driving me away). Anyway--most parents do come around in time because family is so important to us. She has a tough pill to swallow right now, and nevermind that she can also credit herself for raising a healthy, empowered daughter....perhaps that realization will come in time.
Let your own reaction have time to fade. Enjoy your baby and just let this go for now. Consider this a needed 'time-out' for you and your mom, and let it be as happy as you can. I guess that things will come around in time.