Never travelled long-haul, so any advice is appreciated:

We're planning to go to Maui (OGG) from Kiev (KBP) in business class with UA/LH. Getting there seems rather uncomplicated as we'll fly out to LAX via MUC, overnight at a friend;s place and continue to OGG the next morning.

Coming back is tricky. We'll be leaving OGG in the evening arriving LAX in the early morning (around 5am) then we have two options:

1. Immediately continue to either ORD or IAD, connect to to FRA, arrive to FRA the next morning and continue to KBP in two hours. Which brings us back to Kiev around 3pm giving us time to unpack and unwind before going back to work the next day.
2. Leave the airport and head to the friend's house, where we can nap and take showers before heading back to the airport to catch a firect flight to MUC, we'll then have a 6 hours stopover in MUC (I'm a visa natinal and can't leave the aiport) where we, again, can take showers in the lounge and relax. However, we'll be back home around midnight.

So, the first way gives us shorter connection times and earlier arrival home, but four flights in a row without a chance of a shower.
The second way is less hectic giving us plenty time in between the flights and acces to shower on at least two occasions.

What would you chose? Any input is greatly greatly appreciated...