PRC-Russian co-operation is merely lukewarm.
On the contrary, I think the relationship between China and Russia over the last few years has become quite warm. Still realist, but also still warm, with no meaningful disputes of any kind.
And let's be honest here, for Russia, the relationship with China has been the most productive, positive and receptive major power among any of the world's powers especially after Crimea, and I'm sure Putin remembers that.
The US can easily keep that cool or dampen it further through adjusting its direct relationship with both countries as well as influence allies' and other countries' relationships with the two. Time will tell who gets the last laugh.
What you described is just general international diplomacy. For your previous post to be considered, we would have to look at what realistically the US will need do to achieve your suggestion and what the US realistically would be able to achieve, versus what Russia will be willing to accept as a US offer and also versus how much they would be willing to degrade relations with China.
And on balance I think there is very little reason to believe that what a Trump presidency can offer to Russia would be enough to turn Russia against China, especially considering the US will still be there after Trump leaves the white house eventually in four or eight years time, and the US by then will still remain the world's most powerful military and the institutional think tanks and establishment hawks will almost definitely still hold the same view against Russia that they do now.
If anything I expect Putin and Xi to coordinate a little to maximize the benefits their two countries can both gain by playing Trump.
So really at this stage I think it's waaay too premature to suggest that a Trump presidency will mean Russia will join up with the US and turn against China(???), not only because we have no idea what Trumps actual foreign policy will look like (meaning the most likely answer we should be saying is "we don't know"), but also more importantly because the things the US (even under Trump) can afford to bring to the table for Russia will almost definitely not be enough for Russia to degrade its relationship with China let alone actually turn on China.
I'm actually very confused as to why you believe this is even a realistic prospect to begin with, because there has never been any indication by Trump that he would be interested in joining with Russia against China, nor do we have any reason to think that Putin would be interested in joining with the US against China either, especially when the biggest threat to Russia's security and interests will continue being the US rather than China, during and after Trump's presidency as well.