We were on the M/S River Melody, a sister ship to the Rhapsody, on the Great Rivers cruise last June. Internet access was very unpredictable throughout the voyage. It was usually unavailable between ports and even while in port at times.
Much of this was caused, I believe, by the many travelers with iPads. Imagine 50 to 100 people on the boat all trying to access the Internet at the same time. That number may be exaggerated but iPads were certainly in evidence in the lounge. I would not plan on using Skype video at all, and perhaps not even a Skype audio call.
That said, when available, we did have access in our cabin. Access tended to be better a night and the boat was not sailing between ports (which it often does). And, we often found cafes with WiFi that we used during free time in towns along the way.
Enjoy your cruise! You will have a fabulous time.