Kiki hates the Monkey King. They have been fighting. She wants peace and wants her children to grow up healthily (Sun Wufan was forced to study instead of training when he was a child). When Sun Wutian was born, Wukong was dead and the world was at peace. Sun Wufan naturally won't specifically ask Kiki to allow Sun Wutian to practice martial arts (in fact, Kiki only taught Sun Wutian some basics, and even the Super Saiyan won't allow him to change). Moreover, Sun Wufan didn't know how Sun Wutian's martial arts were before the first martial arts meeting in the world, so he didn't teach them specifically.
Vegeta is a man who pursues strength and will train Torankusu.