First of all, I would use italics, to indicate that these words are not spoken aloud, but are not part of the narrative. Every time I see quotation marks, I assume dialog, and if the words were directed toward another person, it would sound even more like that.
Secondly, the first time you see the twins doing it, can you describe what it is they are doing? Maybe they use a certain word for this, a word which would be their own.
Jo [interesting, pretend verb]ed to Andrew, Don't worry. They will never find out. It's only for you and I.
I'm sure you can come up with a better verb than I could. or:
Jo told Andrew, Don't worry. They will never find out. It's only for you and I. Andrew knew she was right, because she said in to him in that way that no one else could hear. He never noticed it when he was a child, because it sounded the same, either way. But when he got bigger, he realized that their mother could not hear what they said when they spoke without moving their lips.
Obviously, you know more about your characters that I do. This is just an idea. If you describe it something like this, it will not only show what they are doing, but show how it feels from their perspective. They might not describe it the same way you would, if you can't do it. How does it feel to them? Did they try to speak this way to everyone, and then notice that no one else could hear? Or did they always know, instinctively, that this special way of talking was only for each other? How did they discover it? Did one of them think something, and then realize that the other one replying to their thought?
