When you do decide to tell them, if you want to do it all at once, rather than two times, try and arrange a meeting with both of them together, or breakfast/lunch/dinner.
If you have an issue with losing your train of thoughts or voice, may a suggestion of writing it down to help guide yourself for the face to face interaction to them. Eventually you will need to tell them, the sooner is always the better choice, than later.
I remember just about two years ago when I came out to my family. Of course dealing with my parents, first was my mom, when we were relaxing and watching her soap operas. Of course I knew it would go well, but it was a challenge for me to gain enough courage to get to that point.
For when I came out to my dad, I had arranged a breakfast, along with my mom there too. Of course this may not be the most suitable privacy wise to say something this life realization, but it went well in any regard, despite being in a decent sized open public area, at least the commotion of everything going on made the world around us, not overtly public to everyone else around.
My brother was my most mentally challenging hurdle to come out to. I had put it off for months, before I decided to meet up with him for breakfast at of course a decently public restaurant. Though telling him about everything in the parking lot before breakfast. So then, after the talk, we just had breakfast over light hearted conversation, instead of nerve wreaking real talk.
So anyways, enough of my own story. My suggestions would be to write everything you want to say, and everything you may want to say, set a date to tell them, either at the same time or at different times (depends on if they get along together or not, I am not so much informed on your own family matters as that is not of any knowledge of my own), give it about a weeks time, so you can calmly go over, add things, or scratch things off your checklist. And if you do need to bring your paper with you, for if you get choked up, there should be no issues to come out to them. It may seem to yourself a little rehearsed, but if that gets you to where you need to go, it will be a lot less on your shoulders afterwards.
If this cannot be done, maybe you could do it in a face-time conversation over the phone, in the same matter with a list of what you want to say. If that cannot be done, then over the phone or a constructed letter will also suffice. Needless to say if you go the letter route, they will most likely call you or find a way to talk to you, and then you can open up in that way. Especially after sending your letter would be your own jumping over the initial hurdle to talking to them about it, and may come more natural to talk about yourself.
I hope this helps.
