AlwaysAisle is right in that the fastest way to get to Mt.Fuji is by one of those express highway buses. I have heard good things about some of these one-day bus tours, that they really do have things well-planned out. I don't know how old your folks are, but my mother (late 60's) can never be bothered to take a train to Hakone and do any sort of walking and carrying things. So I can appreciate how some folks would just want to do the bus tour thing.

I think Mt.Fuji 5th Sta by bus then swinging over to Hakone and then wrapping up the day with a ride on Shinkansen is great. It's a bit of a whirlwind, but it'll still work out with a guided bus tour. What I think is a waste of time is the pirate ship ride on Ashinoko Lake. Komagatake Ropeway is okay, but I think a better option would be to do the Hakone Ropeway which takes you over the breathtaking Owakudani and still gives you the great view of Mt.Fuji (if the weather's nice). There're just so many better ways to spend time in Hakone than to do the pirate ship and Komagatake Ropeway imo.