So how was Padme supposed to die? Old age? Attacked on a frigate? How would her twin children get to Tattooine and Alderan respectively? Was she supposed to be doing what when she died and they got separated?
You're wrong about Yoda. He DID train Obi Wan. If you paid attention to Attack of the Clones, you see Yoda training ALL of the younglings!! Remember how he had a huge pack of boys and girls, little, training them when Obi Wan needs to find the planet Kamino? Yoda has the kids help out. This is the way the Jedi work. They collectively train under a grand master, then at a certain age go to a specific master and become their apprentice. So Obi Wan was right! Continuity? FINE.
Obi Wan said he decided to train Anakin because of how powerful he was in the Force. Well, to an extent he's right. Qui Gon kept talking up how Anakin was the "chosen one" who would "bring balance to the Force." He kept talking up how Anakin had sky high "midi chlorion" levels. In other words, he was heavy on Force power, and he told that to Obi Wan. Obi Wan fought to have Anakin made his apprentice and seems to have taken to the role. Obi Wan took him on as an obligation to Qui Gon who saw his power of the Force, so Obi Wan saw it as well.
Obi Wan, in a New Hope, says "I don't seem to remember owning a droid." Point of fact--he's correct. He never owned R2D2. He never said he didn't know who R2 was.
Uncle Owen---well, he met Anakin briefly when he visited looking for his mother. Then he went off and was not only into trying to become a Jedi, but he fought in the Clone Wars. Tattooine is an outer rim planet, neutral, and stayed out of the Clone Wars. Uncle Owen was given Anakin's son, presumably told who dad was, and Uncle Owen remembers a dad who went off on a mission to find his mother, killed a ton of Sand People in a crusade to avenge, joined the Jedi order, and left fighting the Clone Wars and never came back. Either that OR he knew Anakin went off to fight the Clone Wars AND turned into Vader on a crusade to conquer the galaxy for the Empire and bring order. Crusade could be Clone Wars, Jedi, sand people conquest, or Imperial fanaticism and switching to the Dark Side. Take your pick. Again---continuity fine.