Topic title. I want to take Riften back and put Laila Law-Giver back instead of some Black-BerryBriar

If you side with the stomcloaks in the war then yes.

Also Law-Giver is a pawn of Black Briar its the same person ruling either way

Better see an innocent Law-Giver instead of a corrupt Thieves Guild Grand Master. It won't change Riften, but at least one good person is up there

She isnt good though.

Good person? She disgraced her son for voicing his opinion on the civil war! True, Mavin is a really bad person but at least she won't have the benefit of remaining hidden in the shadows anymore.

No, but she can do things like tax goods or place innocent people in jail without evidence. Law-Giver is more misinformed rather than corrupt. Her steward is the corrupt one.

Riften, like Markarth, is basically screwed either way. The jarls they begin with both mean well, but they have corrupt stewards who hide from them the fact that they're not actually in charge of anything in the city. And then in Season Unending you most likely end up replacing both of them with the people who are actually running things, which can only make those cities even worse places to live in. And you can only redeem one of them with the civil war quest, because Jarl Laila is Stormcloak and Jarl Igmund is Imperial.

People choosing the lesser evil (ie the less corrupt, ass mouthed Jarls) should:

-Don't play the civil war quest line
-In Season Unending trade the Markath hold for Dawnstar and Winterhold instead of Riften.

To obtain both the small holds without Ulfric or Tullius abandoning the peace conference in protest the other issues should be chose so that neither side feels too much penalized.

In my game, it's always Tullius who spoke first, and he always wanted Riften :/

I don't know why...

Stratigic value which he actually explains

No, I'm referring to the part that it's always Tullius who speaks first, not Ulfric. While the page in UESP (and msxyz's account) says that it's Ulfric who speaks first (and further says that Tullius gets enraged because of the amount of silver there)