First a short update on the broken extremeties: It was indeed a clean fracture of the left radial bone.
The accident happened in Nara on Tuesday evening and mom firmly believed it was just a sprain. So we went back to Kyoto to catch our Shinkansen to Tokyo. Partly due to the accident and partly because we didn't take the rapid local service, we arrived in Kyoto too late. There were only Nozomi trains going back to Tokyo. Since the JRPasses cannot be used for those, we figured we could get a decent hotel for less than the price of a Nozomi ticket. And because we didn't know our way around Kyoto and Gen already reported no available hotel rooms in the city or its vicinity, we went back to Osaka. We hoped that our hotel there would have a room for us for one more night, but even if they didn't, they would at least offer Internet access which we could use to find another hotel or a way back to Tokyo.
Of course there weren't any rooms available anywhere in Osaka that were affordable and reachable at 11pm, so I had a moment of panic. I tried to figure out if there's a bus service we could use, but I couldn't get any useful information on that option, either. So in my desperation I checked Hyperdia again for a connection from Osaka to Tokyo. (The JR Travel Center in Kyoto told us there was no other connnection available that night except the Nozomi.) And lo and behold, there was the Sunrise Seto leaving Osaka Station at 0.34h (= a time we could make without problems) and arriving in Tokyo at 7.11h (a time when local JR lines were operating again and we could get to the hotel without further delay). On top of that, we could use the Sunrise Seto with our JR Passes, we didn't have to pay anything for a reservation and there were exactly 2 bunks available on the lower row, right next to each other (mom couldn't climb ladders with her broken arm). On our way to the station we had stopped at a combini and stocked up on comfort food and beer, so we had a late night meal and went to sleep. :)
Back in Tokyo we went to the hotel first. Mom took a quick bath and I looked for a doctor or clinic. I found the
Tokyo Medical and Surgical Clinic. With their multilingual staff, recommended by embassies and located near Tokyo Tower (easy to reach, familiar area) it seemed like our best bet. And indeed, it turned out perfect. We entered the building 12.05pm and we left at 1.06pm with a professional cast. We spent about 47,000 Yen for consultation (surgeon), two rads and a cast set by the surgeon himself. I think that's a pretty decent price and we also checked with our travel insurance and they assured us that they will reimburse us the entire amount without any questions asked once they receive the bills.
So I learned a lot about getting around in Japan, and I can really, highly recommend TMSC. The staff was very friendly, very professional and very efficient. They have pretty much all the specialists and equipment under one roof, the entire staff is fluent in English and they don't overcharge foreigners just because they can. Payment is accepted in cash or by credit or debit card.