Is there a diving liveaboard boat that goes to both Yap and Palau?
Colonia, Yap
It's possible, but I'm about 99.999% sure there isn't. It's almost 300 miles from Yap to Palau, so it would require either a significant r/t, or alternating the starting and ending points of each trip. I just don't imagine that happening.
I've done a trip to Yap and Palau, and highly recommend it, but you should figure on flying to Yap and doing a land based trip, then on to Palau. The consensus seems to be to do Yap first so that it doesn't seem like a let down after Palau. Not that the diving in Yap isn't great, but Palau is even better.