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I do not agree. It was Anakin who betrayed Padme by joining the dark side. Their alliance was with the Republic, Anakin joined the enemy hence betrayal... Anakin was a massive emo. Very emotional unstable and emotionally weak, that led him to being easily manipulated by Palpatin with mere manufacturing of imagery of Padme's death.
Obi-wan didn't hurt Anakin. Have you forgotten the scene annie choked his wife that he's supposed to keep safe? He left her unconscious from that choke cuz she won't follow him
That is before the duel. This showed Anakin had been corrupted deep, Obie refused to join either and that prompted obie and annie to fight. He lost the duel and nearly burned to death... Meanwhile Padme being unconscious was brought to the asteroid place after the duel. She was healthy upon arrival explained by the robot droids yet she was dying. That's because palatine ''siphoned the Living Force from Padmé and brought it to Anakin'' as this analysis suggests www.retrozap.com/.../
which is plausible very much. Further manipulation was done by palpatine by telling Vader that he killed her. Vader being stupid as he is believed it despite his strong senses telling him that ''But she was alive, I felt it!''
Most importantly, to answer your question the answer is no. The war had nothing to do much with their personal lives. The aim of the empire was to invade, conquer and rule the galaxy and beyond. The rebel resistance would have still continued on even if Padme joined Anakin. Oh and to conclude, Anakin was a massive emotionally idiot who didn't save his wife but got her killed!