Many people would argue that someone's address shouldn't determine the quality of public education that is available to him or her. While it is unfair for your sister-in-law to lie about her address and get into the charter school, it is also unfair that someone who lives in one area has access to better public schools than someone who lives in another area. Thus while you are not breaking any rules or cheating, you are certainly taking advantage of a system that basically gives people with wealth better access to great public schools, while providing limited access to poor people. It is hard to say that this is a fair system by any stretch, yet you seem to have no qualms using it to your advantage, as most people would (and I would as well).
Economic equality is a fantasy of socialist utopians; equality of opportunity, however, is a bedrock principal for a healthy and successful capitalist society. It is hard to imagine something that prevents equality of opportunity more than a public school system in which many poor yet talented children receive a lousy education.
On top of this, cheating is so rife in the public school system as to make what your sister-in-law did pretty minor in the grand scale of things. People use other addresses all the time, or even rent tiny cheap apartments. Even worse, there are an increasing number of wealthy parents who get their children diagnosed with learning disabilities in order to have them be provided certain advantages on tests. In some areas, there are more kids diagnosed with learning disabilities from wealthy backgrounds than poor backgrounds, which is likely not a reflection of reality. There are professionals who write college essays, volunteer "service projects" that are awesome on the resume but only affordable by the wealthy, etc.
My point is that rather than trying to take on your sister-in-law, which will do little to improve the system and likely cause family strife, think about using your anger to help effect real change in our public school system, especially in ways that get better teachers and better schools and better learning into poorer districts. Might be though with a young family. My own children are 12 and 15 and it is hard to do anything but focus on them. But I know that the day the younger one goes to college, I am going to start using all the tutoring skills I developed as a dad to help tutor kids who probably need it more than my daughters.
Best of luck to you, your family and your sister-in-law's family, and most importantly to all those other families who don't have the opportunity to lie or move to get a decent education for their kids.