i am a storm cloak and i just took over whiterun. you would think ulfric would excute the jarl to show what happens when you support the empire

I expected that, too, especially since when you find Balgruuf later in the Blue Palace he's talking about wanting Ulfric's head on a pike. I also expected Elisif to get the Helgen treatment. I guess Beth thought that would be a little too realistic. Ulfric wants to be as conciliatory as possible, though- he was reluctant to attack Whiterun in the first place and argues with Galmar that their patience was winning them allies.

yeah I'm thinking that too if bethesda puts all realism in one game they can't add little by little in a new game . Ya know?

What doesn't make sense is that Ulfric lets Balgruuf pack his bags and leave, but doesn't allow him to take his children with him. Well, only one of his children goes with him. He says the others were "lost" and that he hoped one of the servants are now taking care of them. I don't see why the guy couldn't have found his children before he left.

His children are awful, probably thanks to daedric influence, but still...

And there's your answer. Having met them myself I'm not at all surprised that he managed to "lose" them on his way out of town.

And to be fair, Ulfric wasn't there. If he gave orders for Jarls and their families to be spared if they surrendered, then those orders were followed. Why Balgruuf didn't take all his kids with him is never explained or even alluded to AFAIK. Maybe they were kept there in the custody of those that Ulfric trusted as a way to curb any thoughts Balgruuf might have had about retaliating once he got away himself. It wasn't all that uncommon in "olden times" for rulers who were not actively hostile to each other but still mistrustful to have some of their children or other close relatives living in each other's courts, under each other's "protection," as a way to ensure continued good behavior on everybody's part. So maybe it was something like that.

I imagine it's just because one of them is involved in that quest. Other exiles will still give/ complete quests, but that kid's dialogue wouldn't make sense outside Dragonsreach ("I know all about this place" etc.)

Why doesn't Ulfric kill his captives?

Ulfric's victory will not come from killing his enemies. He must achieve legitimacy. His allies serve him because they believe he is right, and that he has the best interest of the people of Skyrim in his heart. And indeed, though I believe him power hungry, I also believe him sincere. If his allies did not believe this, they would abandon him.

So he can't just go around killing whomever he wants. Every death must be calculated. Killing has the potential to reduce the legitimacy he seeks, so he should spare his enemies when possible. The other side can afford to seek his head; he is a traitor, and the penalty for treason is, in pretty much all places and times, death. Ulfric's position is different.

As to the kids, Ulfric is probably keeping them as hostages... not an uncommon practice in such times and places.