teaching with integrity or... just putting in the time

I'm out here in South Korea trying to make money, because the government of Canada demands that I pay back my loans. The goal of this year long excursion is to save money enough to end my debt and perhaps return with some money to boot. Of course there is the minor goals of traveling, and experiencing life and culture, but I suppose that these are second to the main goal of saving some cash.
So... how does this fit in with what I actually do here? I teach five days a week; I am the reason the school attracts it's students (the promise of a foreigner's native tongue). But these kids are anywhere from five to fifteen years old. The children want to be children and run around (so they should) and the older ones want to be anywhere else rather than the English Hagwon (academy). I'm realizing as I spend more time at the front of the room that these kids are... just kids! It should have been obvious, but... no it wasn't. I entered the English teaching field with the high hopes of teaching kids how to communicate, but I feel like that goal was set a bit high.
These are just regular kids. At five years old how many different languages did you know? How many different schools did you attend? These kids are worked hard! Trust me, I'm an optimistic person but they will not (most of them) be able to pick up a new language, even if they are pushed as hard as they are. So all this was to say that I have come to a conclusion (or, perhaps a more realistic goal). I will just be there. I will teach what I can, but also play the games. I will run through the curriculum, feeding the kids only what they can handle.
Sounds like the right answer? Maybe, but I feel like I'm taking the easy way out. And it WOULD be the easy way out. It's ridiculous trying to get them to follow any type of structure, or respect. Especially the little kids: back home these kids would be having a nap time, where here, they are learning how to chat about the weather in a foreign language. Have your break kids. Let's play a game.
But my other problem... The older kids, who have the potential to learn and to develop in their English. I can think of one class especially where the balance between teaching them and tolerating them is like walking a tightrope. On one hand there are some people in the class who are picking it up and want to learn. On the other, there are a few who don't want to be there, and swear at you in Korean because you tell them that they can't listen to mp3's in the class. Do I just let things slide to make it easier on me and them, while sacrificing their English lesson? or do I stand my ground and have fifty minutes of hell telling the few of them to behave? I was once told that I should just "do my time" and then come home. I'll get paid either way, but I feel that I can't just let the class run itself. There's much potential for knowledge there that I feel that it is my responsibility to run a good class. The other teacher that has this one particular class just lets them have their way: if the kids don't like the seating plan, then this teacher will cater to the kids. How can I contend with this and go against the other teacher that teaches 80% of the class? I feel like if I stop trying it would be so easy to just play games with them every class - but I'd get NO respect, everyday... I'm not sure if you follow what I'm writing, but it is a bit of an issue that I've been dealing with the last few weeks. How much effort should I put in? What difference is it making? The battle between having integrity, and having an easy year is war, a balance. I'm not sure which side will win...