I think the following two options would be most convenient:Option 1:
Trains from Kamakura via Ofuna and Kozu to Gotemba Station (90 minutes with good connections) and catch a bus to Kawaguchiko from there (70 minutes).
Option 2:
Shonan-Shinjuku Line from Kamakura to Shinjuku (60 minutes) and Fukikyu Bus from Shinjuku to Kawaguchiko (100 minutes)