MY FAMILY LEGACY: When Jade targets a character in hindering terrain with an attack, Jade modifies her attack value by +1 and the target can't use Stealth this turn.

Jade already has Improved Targeting: Ignores Hindering Terrain

So my question is, how long can the target not use Stealth for? The rest of the turn? Does she need to actually hit?

Not trying to be rude but did you see the end of the sentence where it said ".....this turn"?

Also she does not have to hit the character.

It would not consider it rude. I was expecting an errata or some kind of ruling that is not shown. It just seems pretty ridiculous, but very helpful.

this site is usually pretty on it when it comes to erratas being added to units. right now, nothing is showing, so play it as it reads!

OP take note of that distinction as it is very important not to assume similar effects work the same.

KRYPTONITE ARROWS: When Green Arrow hits with a ranged attack, the hit target can't use defense powers until your next turn. If the hit target has the Kryptonian keyword also give it an action token.

vs.

SWORD OF FAITH: Opposing characters can't use defense powers when they are the target of Iron Paladin's close combat attack.

The difference between target and hit here is very significant.
Against the first power you can still shape change, prob, super senses or other evasion before defense powers are turned off. Where the second one only allows shape change and prob.

Another example;

tmts021 axe -EFFECT: This character's attack rolls of 10-11 that hit count as critical hits

vs.

HEX MAGICK: Give Scarlet Witch a power action to attach the Hex Magic marker to a character within range and line of fire, removing it from anywhere else. If that character is friendly, when that character attacks, a Critical Hit is an attack roll of 10-12. If that character is opposing, when that character attacks, a Critical Miss is an attack roll of 2-4. When Scarlet Witch is KO'd, remove the Hex Magic marker.

The effects of the axe only matters if the attack naturally hits on its own where the hex marker doesn't care if a 10 would have it, it does now.

There are several other examples of these somewhat subtle differences but the point is that there are devils in the details.

Its not ridiculous at all. Jade has improved targeting which ignores hindering. Her power which stops the targeted character from using stealth the remainder of the turn is helpful to her teammates who may not have improved targeting capabilities.