I've not really had a similar family situation but it seems like none of us do? We have some fundamental similarities but all of us are so different and everyone's lives are so unique it's hard to draw comparisons with others.
I grew up very obviously not normal, I struggled and failed to be a boy and my parents were very aware of this and compassionate and understanding. I was given every opportunity to express myself as the girl I was while also being presented with, if not encouraged toward more masculine pursuits. I know my parents hoped this all was just a phase or something I would grow out of but by the time I was 14/15, it became obvious that was never going to happen.
Allowances had already been made and with my folks help, I stretched the rules as far as I could. I couldn't understand why I couldn't look like other girls which as a child, for me focused not so much on clothing but on having long hair, Before the 3rd grade, I was allowed to start growing it out which combined with my personality and manner really set me apart and made not only my behavior, but my physical appearance as well quite out of the ordinary. Needless to say, this made my life quite difficult socially and caused nothing but problems with school and the world at large. I was denied enrollment in junior high/middle school because of the way I looked but my folks were there and fought hard for me with lawyers and psychiatrists and managed to smooth things over.
The terminology was different back then and things much less well defined but In today's parlance, I "came out" to my folks at 15 in 1970. It was more a case of getting everyone on the same page because they already knew who I was and where I was headed even before I understood it all. By that point in time, I was slightly more than completely androgynous but with all having the common understanding that there was no way in hell I was going to grow up to be a man, my folks did what they could to help ease my discomfort allowing even more outward changes even though it only pushed my social ostracization to the extreme. By the time I was 17, they had found a specialists and I began HRT before my senior year of high school. After graduation, they did every thing they could to help completing my transition including arranging for my name change, etc. They fully supported and loved me as their new daughter and did their best to give me some sort of normal life in every way they could. Nothing else made sense.
BUT, when it came to surgery, my mother considered it to be mutilation which was quite confusing to me because my folks had been so completely supportive and helpful otherwise. I couldn't understand how she expected me to live that way? I sure as hell couldn't and when I finally did have things in place when I was 22 (1977), she refused to go with me and we had the biggest knock down, drag out fight of our lives about it. I flew out of state and went through surgery and 8 or 9 days in the hospital alone. I was so angry, I didn't speak to my mother for 8 or 9 months after.
Through the mediation of a cousin, we finally did make amends and I got invited to my folks house for dinner one evening. At the table, nothing was discussed other than TV shows, car problems and the weather. It was weird and strange and the elephant in the room was ignored. After our meal and I did the dishes, I dragged my mom by the arm into her bedroom and made her look at my "mutilation".
She was beside herself. She had no idea that surgery would make me into a "real girl". She hugged me and we cried. She realized how this made me into a whole person and that I really did have a chance at a new and better normal life. She apologized for not helping me through surgery and for all the things she tried to do when I was a child to make me be like a boy. It was one of the most touching moments of my entire life.
You have to do what is right for you and not what it is that will make your parents happy. It is your life, not theirs. If they've seen how much better things have been for you with transition, it may take a while but they should be able to see you'll be better off after surgery as well. Although it is really a matter of functionality, congruity and peace of mind with your own anatomy, they may indeed still consider it "cosmetic" but the depth of how it is life changing for the better is undeniable. If they're understanding and intuitive at all, they will see this and come around.
Yes, a lot of this does depend on the parents you have and the people they are. They may not understand it and be against it but if they love and care about you, they should be able to see how fundamentally better your life will be as a whole complete female person rather than some in-between hybrid. That was my experience anyway, for what it's worth. YMMV
