While I was writing up my post about the Chosen one prophecy, I started writing about how I felt Qui Gon would have trained Anakin had he survived his duel against Maul, so this is what I ended up writing: 
If Qui Gon lived to train Anakin, it’s possible Jinn would not approve of the way Anakin was being taught amongst other younglings, and the way the Jedi started to become political figures and soldiers instead of keepers of the peace after the Clone Wars begins. I think he would take it upon himself to train Anakin outside of the temple (meaning walking away from the order completely) and slowly blossoming Anakin to his potential through means the Order would not use. It would be cool if Qui Gon sensed something odd about Palpatine prior to leaving the Order, and instructing Obi Wan to keep a close eye on the Chancellor.

Once Qui Gon felt Anakin was wise  and strong enough to bring balance and destroy the sith, he would bring him back to the Order to search for the hidden sith and aid the Jedi in the war (even though Qui Gon did not approve of the ongoing war, they had to end it in order to find the remaining sith). By this point I think Palpatine would have a new apprentice ( not really sure who, maybe Dooku or Ventress since Maul would have ended up dying in a storyline where Qui Gon survives [or Obi could just cut him in half again in their duel, but not the point] ). He has a new apprentice that has been serving him throughout the CW. So whoever the apprentice is has to encounter Anakin and he tries to find out if this is the sith they’ve been looking for or if it’s another assassin/apprentice. He fails to find out from this person, until Palpatine discards his apprentice in an attempt to persuade Anakin to the dark side. Of course, Anakin is a different man under the training of Qui Gon and picks up on his feeble remarks and starts connecting the dots. Master Kenobi  (now training Ahsoka since Anakin wasn’t present on the battle of Cristophsis to take Ahsoka as his padawan)  tells Anakin of Palpatine’s suspicious demeanor towards the Council, seeming to want to be in office for longer than his term. To keep it short, Anakin confronts Palpatine with the other Jedi Masters (yes, he would be considered a master finally)  and Palpatine would be defeated. Anakin finds his love interest in Padmè once again with Qui Gon allowing Anakin to embrace his attachment. He would raise his two children, Luke and Leia outside of the order with Him and Qui Gon being their mentors and living a free life with his wife away from the Order. It  still took the Order years to realize it’s faults under the clone wars with politics. It is Only when Qui Gon returns to teach them about their mistakes do they finally revert back to the ways of the old Jedi where they were not restrained by harsh Dogma.

Realistically, Palpatine would have Qui Gon assassinated in some way before he leaves the order to train Anakin. Sheev would do anything in his power to influence the chosen one to do his own bidding. But I really enjoyed coming up with this alternate timeline where Qui Gon lived to train the chosen one. 
I will start working on Rewriting Kenobi from the very beginning soon as promised. Thank you guys for all your support on all of my posts. Very much appreciated.