Thanks.

Believe it or not, but IOTL, from what I can tell, there were calls among some Taiwanese to place the islands under UN rule or American rule. By placing it as a Trust Territory, they both would mean the same thing, as was the case with the TTPI.
What would the PRC be doing in this scenario?
For Taiwan in particular, it all depends on several factors, among them how the Chinese Civil War progresses. Before we get to the PRC, let's assume a scenario similar to OTL where the ROC still exists - however tenuous its control - and thus Jiang Jieshi retains power. Obviously, as a founding member of the UN, Jiang would obviously not be happy about this, since to him (and many other Chinese nationalists) of course Taiwan should be returned to China ASAP. The only way in that case to placate Jiang is to induce incentives for him to accept trusteeship - and plus, as a founding member of the UN, Jiang would have a say over how Taiwan would be run, even if indirect. Now, for the situation you're thinking of for the OP where I think a UN Trust Territory could work, the PRC is in a bind of its own. On one hand, they'd probably complain, but on the other hand (unlike OTL) there will still be difficulty trying to maintain control over what existing territory it had. The PRC would be in no situation to accept Taiwan at that moment. So the PRC would be preoccupied elsewhere. Which brings me to:
Obviously, they would not agree with the UN's decision to "trust" the islands to the Americans. This basically puts them in situation in which is them against the rest of the world.
The only way I could see the PRC agree with the UN is if the trusteeship is temporary - which is part of the nature of a trusteeship. Say, give it about 50 years, so if we start the trusteeship in 1945 then it should end at around 1995. In that case, as the trusteeship comes to a close, that's when the decisions will have to be made. What will happen is anyone's guess; I'd love to see an independent Taiwan come out of that scenario, but all options would be open. If there would be no agreement on what would happen come 1995, then there could be a possibility (though I don't know of any precedent) of extending the trusteeship agreement unless the situation is resolved.
Could they even refuse to join the UN in this scenario?
If they want to - no one's stopping them from joining ITTL.
How would the normalization of China's relations with the west play out?
That I do not know.
Would Taiwanese independence be more or less likely compared to the scenario in which there is a "normal" US occupation?
For all intents and purposes - yes. The only differences between a trusteeship and a "normal" US occupation is that in addition to being part of US jurisdiction, it would also fall under the authority and supervision of the
Trusteeship Council. Which would mean, like the Japanese colonization of Taiwan beforehand, that the US would have to put on its best behavior when it comes to administering the colony. At least more so ITTL considering the OTL behavior of how the TTPI actually occurred, where the UN criticized the US for basically doing nothing to improve the islands and thus failing to prepare them for independence. Taiwan would ITTL be the US's "model Trust Territory" to deflect criticism from the TTPI, which would mean that Taiwan would probably have it better than, say, Puerto Rico or the Philippines.