The problem is, if you are reading a book whilst Skyping, you can't look at the screen at the same time, so you can't see how she is reacting.
Perhaps you just have to skype at a different time of day, she is are more attentive or perhaps you could video yourself reading and the parents can sit her down to watch the video when she is in the mood for it. Don't forget to show the pictures to the camera as you read, with your face in view and your hand pointing at the relevant parts of the pictures.
Working out the technology for recording and sending the recording may be a challenge, but we can't let ourselves be beaten by something like that!
Children don't quite get the concept of sitting and talking about things, so it may seem just plain tedious to them, having to sit face to face and just talk. On the other hand, there are, of course, those like the young lad described by madamecholet, who will hold a lengthy conversation on the phone.
I shall be looking into that Caribou - sounds brilliant!