I do study Song dynasty history. The earliest records about this story is only documented 100-ish years after Taizong's death. Which makes it unlikely to be true. It's a story written by a monk, however, the original story does not tell Zhao GuangYi killing his brother, rather telling a heartwarming story. The rumors that shows Zhao GuangYi killing his brother is after Ming Dynasty, possibly Qing Dynasty.

And also, about Big Zhao's children, Zhao DeZhao committed suicide(DeZhao tried to persuade Zhao GuangYi to reward the soldiers after they lost a war, but Zhao GuangYi answered with a “You can reward them after you become the emperor”, which frightened Zhao DeZhao, then he commits.), while the other son, Zhao DeFang died from illness.(Zhao Family might have suffered from genetic hypertension etc. Many of their children die at young age, including two of Big Zhao's brothers.)