Is the damage of a Battle Master fighter's Sweeping Attack maneuver doubled on a crit to the 2nd target?

"With this Maneuver in particular the phrase "with the same attack" is used; you are not making a new attack, and so the damage from the superiority die is also part of the original attack's damage roll."

also, the maneuver text doesnt say you add the superiority die as damage to the primary target. Other maneuvers where that happens, is stated out that it adds to the damage.

If that were the case, the sentence would be something like this: "When you hit a creature with a melee weapon attack, you can expend one superiority die and add it to the attack's damage roll. You then attempt to damage another creature with the same attack."

The Superiority die here is not affected by a critical hit

The section on "Critical Hits" states (emphasis mine):

When you score a critical hit, you get to roll extra dice for the attack's damage against the target. Roll all of the attack's damage dice twice and add them together.

The Sweeping Attack Maneuver states (emphasis mine):

When you hit a creature with a melee weapon attack, you can expend one superiority die to attempt to damage another creature with the same attack. Choose another creature within 5 feet of the original target and within your reach. If the original attack roll would hit the second creature, it takes damage equal to the number you roll on your superiority die. The damage is of the same type dealt by the original attack.

Note that with various other Battle Master Maneuvers the superiority die's damage is rolled twice because the damage from the die is part of the attack's damage roll.

With this Maneuver in particular the phrase "with the same attack" is used; you are not making a new attack, and so the damage from the superiority die is also part of the original attack's damage roll.

It would appear then that you do roll the die twice; however, the critical hit section says that you double the damage "against the target" (note that it is singular). The second creature you are hitting with this attack is a new target, different from your original target, and so the damage that comes from the superiority die is not affected by the critical hit with this Maneuver.

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This is slightly supported by Jeremy Crawford's now unofficial ruling on critically striking with the green-flame blade spell:

Q. If you critically hit with the attack part of Green Flame Blade, and are greater than level 5, do you roll extra dmg against the 2nd target?

A. The splash damage of green-flame blade isn't affected by the attack critting. Think of the attack as process X & the splash damage as Y.

Here he uses a different line of reasoning for why the damage is not doubled, but it is a similar situation.

The second hit doesn't benefit* from the Critical Hit.

Let's look at the wording of Sweeping Attack:

When you hit a creature with a melee weapon attack, you can expend one superiority die to attempt to damage another creature with the same attack. Choose another creature within 5 feet of the original target and within your reach. If the original attack roll would hit the second creature, it takes damage equal to the number you roll on your superiority die. The damage is of the same type dealt by the original attack.

My emphasis in bold. You're not making an attack against the second target, you're checking to see if you're able to deal an amount of damage to it. As such, it can't benefit from the effects of a Critical Hit.

*Well, that's not entirely true. If you rolled a Critical Hit against your first target, then it would certainly hit the second target, regardless of AC, so the "benefit" of guaranteeing the attack connects is still there.