Just FYI, I am fairly certain that the PNR you gave to the CA agent is that of US. There is also no such thing as an 'international ticket number', 037- is US ticket stock and 999- is CA ticket stock. They need your full name and flights (as you explained to the 2nd CA agent) in order to see your booking with CA.

Re the CA agent hanging up, I believe it was due to your choice of words not to mention the earlier call (relating to the ticket stock) which gave a poor impression. If you told him directly that the hotel staff would speak to the supervisor on your behalf instead of vaguely saying "I can get someone", that probably would've done the trick. It would be meaningless if the Mandarin-speaking only supervisor (which is not uncommon, even at PEK one of their managers I spoke to only knew Mandarin) got on the line with a non-Mandarin speaker.

And maybe they were right - CA can't see your full booking (i.e. SQ leg might not be showing in their system, perhaps due to SQ's systems change recently) so they only offered to get you to FRA.

However, that said, it's very common for operating carriers to ask the customer to contact the ticketing carrier for re-routing on award tickets. But at least in the end, they got you onto the nonstop CI flight and to your final destination.