*hug*
I had to go through all of this fairly recently. Fortunately, I had a positive outcome... more positive than I had dreamed.

Of course, I can't guarantee that you will have the same success, all I *can* do is communicate the place my head was in that gave me the courage to go through with it, in hopes that it might be helpful to you in some way.
First, I had been keeping many things back from my family. Being staunchly conservative, I had never even gotten the courage together to tell them I was bisexual, much less mention any gender issues. I didn't want to hurt anyone; my family had been through enough pain. But not telling them, keeping things secret, eventually drove me away from them. In my head I believed they couldn't love me and accept me for who I was, and eventually this turned to keeping them away because (again, in my mind) they didn't love the real me.
Secondly, I had a lot of guilt and self-hatred going on. This is fairly typical for trans* people... Having determined my real gender was unacceptable, it became something to be ashamed of, to hide. This took years of therapy to get over.
So, I knew it was time to come out to my family when I realized that I no longer *had* a relationship with them. If they were to reject me after I came out to them, what would the difference be? I'd just have confirmation of my fears and still would not have a relationship. If they refused to accept the truth about me, the real me, just because it was painful, then they were people I didn't need, couldn't count on, in my life...
On the other hand, if they really did love me, I reasoned, no matter what, I deserved to give them a chance to get to know the real, happy, fulfilled me. Not just some tragic empty husk without a future.
I hope this might be helpful for you. As far as ways to do it, I strongly encourage you to look at the odds of survival for people with GD that continue to try to suppress or hide it, and the odds of survival/happiness who *do* transition. I can't imagine any parent on earth who wouldn't prefer a living, happy trans* <insert gender> to a dead (emotionally, anyway) <insert bio-gender>. Really, it does come down to that, for many.
Wishing you luck, joy, and peace.