Yes, the Extended Family Chart DOES pickup cousins. And it also picks up parents of spouses, and ex-spouses, and ex-spouses' spouses, and children of ex-spouses by other people.
The Extended Family Chart will pickup everyone in your file that is related to the selected person in any way, shape or form -
1) IF the number of generations selected is large enough to cover everybody. I'd suggest setting it to 99 generations.
2) Detach your wife from her parents or you from your parents or from each other - whichever way works for you.
3) Unselect the box to Include ALL individuals
4) Be sure to do this to a file that has multiple copies backed up.
Use the Person Locator to find a person in the charts. That person may be in more than one "island" chart. The "instances" will let you "jump" that person from one chart to another. A person may be a child in one chart, a spouse in another, or a spouse in multiple charts. The Locator person will change the outline of their box from black to blue.
The chart will start with the selected person and do a descendant chart (I think it selects the paternal line first). Then, each spouse in that chart will get its own chart to the right. Then, each spouse in each of those charts will get their own chart, and so on. Each chart represents a descendant chart "island" from one ancestor. A large file could have thousands of separate charts / islands.
Then, when you have everyone you think you should:
Go through the various screens to export all in that chart.
Then, right click
You now have two files. You should be able to add the number of people in your index for each of those files and it should equal the beginning number in your beginning file index.
I might add that if you have a moderately large file, I would do this before going to bed, or at least before going to lunch. This is a very complicated report for the software and it will take a long time to do. If you have a large file, your computer may not have enough memory for it.