Hey, I felt so strongly about this that I thought I had to chip in.
First of all, I absolutely agree with NYCGori. You guys should help her contact the INS to get help ASAP. A few days back there was an article in NYT about a new policy of the US government to grant asylum for 'battered' women in other countries provided, of course, they meet some very strict criteria. As your guest is already a permanent resident of this country, I am sure with some help from your end she will have an easier time extricating herself out of this unfortunate situation. Her first priority should be to get help from the relevant authorities and to get her her green card back (and probably SSN), then she could go on from there.
Maybe your chachu et al. do not realize that they cannot keep her trapped in an abusive relationship just because of some help they offered to her family in exchange for her hand. I hate to say this but at least in this country women are not considered commodities; they have rights. And, maybe because I am a little biased, I think the law here does tend to favor the fairer sex . I digress but I know of one family where a sister visiting from abroad a couple,who were having difficulties in their marriage, was forced to leave the brother's house after the wife called 911! The couple eventually divorced and the guy had to share his assets with and provide sufficient monthly spousal support to his ex who neither worked before nor after the divorce.
I am not an authority on divorce laws but although the couple I mentioned has children together, I believe alimony, to a lesser extent, is still mandated by law to spouses even if they don't. Since the guy in queston does not work it probably may not amount to a lot. In any case, she might want to file a lawsuit against the in-laws for forcing her to go through the trouble she did. That might leave her with some decent amount of money.
Also she does not have to be completely a burden on you guys. She is probably already eligible for some welfare/ food stamps etc that you guys could help her get. Also get her enrolled in a local community college (all of which I think offer financial aid) for some English/computer classes; she could subsequently go on to study for some associate degree in accounting or something that will leave her better poised to get a job here.
I am sure it is not a very ideal situation for you to put up with this guest but I have to agree with Mcpendo about 'duas'. I think there is also some hadith to the effect that none of us truly believe until we wish for others what we want for us. You know, you and your family will definitely be rewarded by Allah for the help of you guys to this lady in these difficult times for her. However, she does not need to behave like a princess either; gently remind her to lend you a hand in cleaning, not use your stuff etc. Since 'fish and guests stale after three days', there is no need for unnecessary takaluf. Be kind but frank about what is bugging you.
Phew, that was quite long but I do hope things get better for your cousin.