I am getting a bit tired of such tense game-play. Can you guys recommend me a game that is similar in style to Animal Crossing? I would also appreciate it if it had decent replay value/longevity.

On Vita spefically? Theres not much. However there are tons of PSP harvest moons (all ports of other harvest moon games but those are pretty leisurely). The port of save the homeland is actually pretty nice and it fixed a lot of my annoyances with it(such as ending in a year).

Hmm, the closest thing to what you want is probably Ecolibrium, which is a free to play ecology management simulator. It's currently only available in Europe though. Bullion Blitz is a simpler game, but it is supposed to be pretty relaxing ("virtual bubble-wrap"), though it's a PlayStation Mobile title so it's not available in all countries.

You might find Knytt Underground appealing. It is a metroidvania style 2D platformer, and while it does have some tricky spots, a lot of it is just exploring and enjoying the atmosphere.

"Frobisher Says!" is a good time, available for the low price of free. Absolutely nothing like Animal Crossing though, I can't think of any recent Vita games that fit that category, sorry. There's Little Big Planet for the Vita, if it's that build-it-yourself aspect you're after.

New Little King's Story could be defined as leisurely. I wouldn't necessarily recommend it at the current sale price as the framerate chugs but it doesn't require a ton of thought to go into it. Very approachable but it can get difficult if you really want the challenge.