I don't know exactly where you want to see when you say "all sights" (there are many museums along the way from Hakone Yumoto to Sounzan, and in areas nearby), but probably you mean the typical round course.
Your hotel is located on the lake, a bit past halfway into the round course, so you cannot really "complete" the course, but I would: reach Hakone Yumoto, take the Hakone Tozan Railway up, stop over at Open Air Museum if you want to, continue on the Railway, onto the ropeway, stop over at Owakudani (for the sulfur site and black eggs), continue on the ropeway to Togendai.
From there: - if you don't have time, take the Odakyu Hakone Highway Bus, or taxi (actually there aren't many buses that connect to that hotel) to The Prince Hakone hotel, located near Hakone-en bus stop. - or, you could take the pirate ship to Moto Hakone, and take another ferry to Hakone-en (not covered by the Free Pass). (If the weather is good, you could try the Komagatake Ropeway from there, not covered by the Free Pass. If the weather is good, the view is impressive.)
- if you have plenty of time, you could take the pirate ship across to Hakone-machi, visit the Hakone Checkpoint, - or you could take the pirate ship further to Moto Hakone, and visit Hakone Shrine. ...then proceed to the hotel, either via taxi or a bit of a walk.
The above depends on what you want to see.
Next morning, take a taxi (probably) to Moto Hakone, and from there, take either Hakone Tozan Bus back to Odawara (35 - 40 minutes ride, one bus every half hour, starting from 10:05 according to my 2012 timetable), or take Numadu Tozan Tokai Bus (45 - 50 minutes ride, one bus every hour, two during summer season) to Mishima station. You can get on JR Shinkansen to Shin-Osaka from there.
About luggage: I would use the "Hakone Carry Service" - if you drop off your luggage at Hakone Yumoto before 12:30, they will deliver same day after 3 pm to your hotel. (I am not sure if the Prince Hotel is covered by this, though.) OR, you could simply forward the big suitcase to your hotel in Osaka, and just travel light for the two days.
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