What if Song China and the Mongols did not decide to Partition the Manchu/Jin Empire and instead the Song China allied with the Manchu/Jin what would be it's consequences on China?
I'm not sure this situation has any great effects. I don't remember for sure, but I think the Song attacks on Jin territory were easily repulsed. A Song-Jin alliance is unthinkable. Maybe, if the Song don't attack Jin, the Jin can free up their forces against the Mongols, but at the same time, those forces might not be enough.
It was not exactly 'easily repulsed' per se. Song army managed to capture Chengzhou and Tangzhou in 1232, the same year as Sanfengshan. OTOH, Jin's forces were definitely not enough to handle the Mongols, the aforementioned 130,000 army were the main force of Jin, and the Mongols easily dispatched them with only 40,000. Jin by itself was unlikely to repulse the Mongols forces as most of her territories (save for Henandi and Guanzhong in 1227) and armies were ebbed away by repeating incursions. After Sanfengshan, the morale of Jin army was shattered and it would be only a little more than a year for the Mongol to siege Kaifeng and Caizhou (with Song) to end Jin once and for all.
And a Song-Jin alliance, while not very plausible, is not really inconceivable. Jin Aizong was an emperor who were willing to cooperate with Song and Xixia (which was conquered soon after Aizong ascended to the throne). The problem was at the Song court. Song Lizong wasn't the brightest or the most industrious emperor you can get and he delegated much of the decision-making to his trusted 'Lixue masters', who in turn weren't exactly the military-genius type of guys.
Then again, the main opposition to Song-Jin cooperation (or at least non-aggression) was obviously the sense of animosity towards Jin among Confucian scholars after centuries of oppression and the memories of Jingkang. But the Song court was not without people with sense. IOTL, Zhao Fan, one of main generals in the court, oppose the joint-invasion of Jin with Mongols. I can imagine a different outcome would come with a different discourse among the scholars, maybe the doves could prevail instead? It would take a lot for the Jin to persuade Song into cooperation, but I think it could be done given enough concessions.
However, the million-dollar question still stands, would it be enough to stop The Mongols? I'm not exactly inclined to think to so…
Yup, that's why my precious post only touches upon whether the conditions are plausible.
And actually I hold similar concerns as yours. The state of Song army at the time was so-so if not in shambles, the track record of Song army against the prime time Mongols was sometimes surprising (like the successful repulsions and forced diversion of Mongol force in the span of four decades after the end of Jin) but was still by no mean stellar (look at the attempted invasion of Henan in 1234 for example), so I hesitate to propose that much difference would eventually ensue, save for the rare event in which the death of some great lords and the subsequent succession crisis that might hold back the Mongols for some time longer. Even in that case it might be only some time before the revival of organized attack.
Yup, that's why my precious post only touches upon whether the conditions are plausible.
And actually I hold similar concerns as yours. The state of Song army at the time was so-so if not in shambles, the track record of Song army against the prime time Mongols was sometimes surprising (like the successful repulsions and forced diversion of Mongol force in the span of four decades after the end of Jin) but was still by no mean stellar (look at the attempted invasion of Henan in 1234 for example), so I hesitate to propose that much difference would eventually ensue, save for the rare event in which the death of some great lords and the subsequent succession crisis that might hold back the Mongols for some time longer. Even in that case it might be only some time before the revival of organized attack.
Yeah, who knows? Genghis might actually get his chance to conquer all of China ITTL, and the physical high from said victory might keep him alive for a few more years of campaigning.
If the Song were more competent and cohesive at that time they would have more chances against the mongols.