4D3N - Hakone (1N) & Kawaguchiko (2N)

Hi, I am planning a side trip from Tokyo and have booked 1 night in Hakone and 2 nights in Kawaguchiko. We would like to get advice on the itinerary and best transportation method from our hotel, which is close to Suitengumae Station. I noted all the research I found online are going from Shinjuku. We are considering to get the 3 day Hakone-Fuji pass, but unsure if that's the best pass in our case since we don't live close to Shinjuku.

Here is my plan so far -
Day 1 - Still looking for the best way to commute from Suitengumae Station to Yumoto Station. We booked our one night hotel at Yumoto.
We plan to get to Yumoto and drop off our luggage at hotel at around 10:30am. Then begin the site seeing clockwise. We have to be back to the hotel (Yumoto) by 4:45pm for dinner. Here are the things/ places we want to do/ go:
- Take the Pirate cruise
- Visit and take photos at Hakone Shrine/ Heiwa no Torii
- Owakudani
- Art Museum
- Gora Park (if have time)?

How much time do we need to spend at the Art museum. Do you think we will have enough time to do the above and can still get back to the hotel by 4:45pm?

Day 2 - check out at 10:30am. Not sure if we can spend much time in Hakone as we want to go to the Gotemba Premium Outlets and yet still need to leave time to commute to Kawaguchiko. Can you please advise the best way to commute from the outlets to Kawaguchiko? I heard the last bus for the day is 4-ish PM.

Day 3 & 4 - we haven't really planned on what to do at Kawaguchiko yet. Any recommendations? The Fuji-Hakone pass will expire in 3 days, so we won't have a pass for the last day. What's the best way to commute back to Suitengumae Station from Kawaguchiko? Is there bus?

Thanks!

You can buy JR Fuji san mankitsu kippu 1 day
=3120 yen,valid JR,non JR, bus ,ropeway,boat
Valid some parts of Tokaido line, gotemba line, minobu line unlimited time for 1 day Whil e u stay in mount Fuji and kawaguchiko area

Just on a couple of points:

open air museum needs at least an hour, but I wouldnt bother with Gora park personally;

I think Kawaguchiko is massively overrated and overpriced but apparently there is stuff to do with theme parks which I didnt see. The only thing that really stood out when I was there - aside from the Fuji views which were spectacular when you could see it - was a hot dog at the cafe next to the doll museum. I'd consider going back for the hot dog, it was truly a masterpiece. Everything else was soso when you have regard to the cost of accommodation there.

Personally, if you are mad keen on shopping I would go to Karuizawa instead.