I am a social worker who specializes in writing psychological reports in immigration cases. Since i see that many people on this board are trying to prove extreme hardship, I would like to share with you some of the 'arguments' that I have used in my expert reports as well as some advice:

First of all, find a good immigration attorney. This is way too complicated to do by yourself! The immigration attorney will decide if a psychological report will help in your particular case. Once hired, the mental health professional (who should be experienced in writing these type of reports, not just your 'regular' psychotherapist) may focus on issues such as:

1.) past trauma to the U.S. citizen spouse or U.S. children of an alien - so let's say your U.S. citizen spouse's father committed suicide, his brother died of cancer recently, and his uncle was murdered. The report writer can then make the argument that if the U.S. citizen spouse loses his alien spouse to deportation, this will be one more devastating loss that will severely traumatize him or her. Mental health professionals know how to uncover such trauma, even if not so dramatic as the example I gave.
2.) separation issues - so let's say the U.S. citizen children of an alien parent have severe separation anxiety because they were separated from you, the parent, for 4 years before they came to the U.S. to live her with you (maybe they were left behind with a grandparent in the alien's country for years before being reunited) even if you go into the bathroom, they follow you. The report writer can then point out that because the children have Separation Anxiety Disorder, they will react very strongly to any separations in the future (like from you, the parent, or from their friends and family in the U.S.).
3.) danger in the country - in my own reports, we document extensively the danger in certain countries that could place the lives of a U.S. citizen spouse or children in danger
4.) stress-related health problems - if the U.S. citizen spouse has a stress-related health condition such as diabetes or high blood pressure (or even if these diseases just run in their family), the argument can be made that they are more likely to develop these conditions with increased stress (like the stress of their spouse being deported or having to move to a foreign country to stay with them).
5.) the U.S. children have special needs, such as learning disability, speech problem, etc. Many countries do not offer good or any special education services.

This is just a 'taste' of many arguments that could be made. My advice is not to try to resolve these problems by yourself, but first to get a good immigration lawyer, and if the lawyer feels a psychological report making some of these arguments would be helpful, to find a mental health professional who specializes in writing these kinds of reports.

Feel free to contact me for more information - my email is ohilly@hotmail.com

Phyllis Gould, LCSW