I'd say Joffrey 16, Sansa 14 and Arya probably 12. Though I'd even suggest Sansa 14 and Arya 13 if possible but whatever. XD

Sansa wouldn't have much to do, which means she's vulnerable to whatever Petyr might want to do with or to her. It could be in that window, that he decides to put his plan into action. If he's under the assumption Ned is going to rot in the cell and die, he could turn his focus onto winning over Cat once and for all, and if it doesn't work, Sansa is a good plan B for him. We're still assuming Petyr and Varys nudged Ned to bring up the incest though it would take some balls to point the finger back at Petyr after everything is said and done.