I would have thought that the only thing that made a visit to Hakone such an attractive proposition for kids was the variety of transport 'experiences' that a Hakone Free Pass gives you access to.
Getting a JTB bus tour doesn't sound even remotely as much fun as mounting all the different trains, cable cars, ropeways ships and buses that form the Hakone circuit with the pass.
I'd definitely recommend the DIY version, forget the bus tour - way too boring!

As for somewhere to stay - how about kokkuminshukusha? (people's or 'national' lodge' - basically, state subsidised inns)
These are generally cheaper and rather more modest than a quality ryokan, families often use these so they should be able to 'absorb' your children better than an expensive exclusive hideaway/resort.
There's a large on in Hakone which might be appropriate: http://www.hakone-lakehotel.com/engl...glishindex.htm