Do international-to-international transfers (ANA to UA) at Kansai require one to clear immigration, or is there a sterile transit facility available?

I've never done international to international transit at KIX. But since no one else is responding, here's some info that might answer you question:
http://www.kansai-airport.or.jp/en/r...int/index.html

Good find. I was looking one level up at the Transit Procedure page. They only list int-dom, dom-int and dom-dom connections. Curiously no int-int.

The airport(s) at which you are transiting: NRT
The airline on which you are arriving: NH (ITM-NRT)
The airline on which you are departing: NH (NRT-LAX)
Your connection time in hours/minutes: 90 minutes
How you are connecting: Domestic -> International
Booked as: Single ticket, from united.com

I know that it's doable, but I can't remember the last time that I've done a domestic -> international connection in NRT.

It is pretty simple and quick. Your luggage (should you choose to travel with that) will be transferred automatically, you will arrive on the ground floor of terminal 1 south, and will just need to take the lift or escalator to the departures floor and proceed to security and immigration. NH should issue your boarding pass at ITM.

For NH to NH, I think you can use the "rapid transit" to go from domestic arrival (3rd Floor) to international departures (4th Floor). Time to transit should be very short. You'll have time to visit lounges or shops at NRT.

http://www.narita-airport.jp/en/guid..._inter_t1.html

In ITM, you'll see a separate check-in counter for domestic to international connection flights. At NRT, just follow the signs. As you can imagine, ANA is set up for this to do it routinely.

Due to JAL SFO-HND schedule change, I now have to overnight in HND airport and take the early morning flight next day to KIX. Should I stay at the Royal Park HND Hotel in the international terminal or the Excel Hotel in Terminal 1? I believe JAL flies out of of Terminal 2. There are 2 adults 2 kids traveling and I am hoping to book only one room instead of two.

I would take whichever one of the two are the cheapest option for the specific night. The airport is pretty compact and getting to the JAL terminal fairly quick from either.

Unless your kids are very young, my guess is you will need two rooms. Hotel rooms are generally pretty small in Japan. But I can't say specifically for these hotels.

If you are taking the bus to T2, might as well book a hotel nearby with shuttle service. Hotel JAL City Haneda, TamaDear Hotel Haneda, Hotel MyStays Haneda, etc all are decent hotels near by with shuttle service.

I would expect Royal Park to be the better hotel, but more expensive.
Is it a 7:20pm arrival at HND? You could still make it onto a Shinkansen to Shin Osaka or a flight with NH to KIX. That would be my preferred option - but I don't travel with children, which makes a big difference .

Flight is booked, can't change anymore without penalty. We could have taken 9:30pm flight to KIX but opted not to rush and just stayed a night at airport hotel. But didn't know both airport hotels are so expensive. Kids are 10 and 11, independent enough but after 12 hour flight they might be grumpy.

With Royal Park I can walk straight in after clear custom, the next day I would have to take a shuttle or Tram I think to JAL terminal.

With Excel hotel, I take the shuttle to the hotel after arrival, and the next day I can take the passage and walk to JAL terminal.

I don't mind spending a little extra so I don't have to take shuttle to hotel than shuttle to terminal the next day, some of the off-airport hotel only run shuttle every half an hour.

The bus connecting HND International Terminal to domestic terminals runs every 6 minutes or so from early morning (starting at 5:00 AM).

Off airport hotels would be cheaper, but with less frequent shuttles. That said, if you know when the shuttle leaves, you can plan ahead.

This doesn't directly address your asked question, but might be helpful anyway if cost is a factor.

the Keikyu railway line is easy to access from international arrivals. First stop outside the airport grounds is Otorii station, which has several business hotels very close that may be a lot cheaper than transit hotels at the airport.