Amy
Great example, and I think people are trying to address this question, but it is difficult. One interesting question is the extent to which the adverse effects of enforcement policies spill over to affect documented immigrants whose social networks may be differentially targeted and who are subject to higher levels of scrutiny.
Maybe you could study this with kids' schooling outcomes looking longitudinally before and after enforcement spikes in their communities. You may also be able to pick up kids' ED visits for specific conditions that could be exacerbated. Often with this type of exposure, you need to find a source of administrative data that is collected as a normal function, either for surveillance purposes (NHANES) or as a function of some ongoing service provision (education or ED medical records). If you can then link that data based on time and place to the event such as an enforcement raid, you can make a pretty good case for the effects of the raid.
Maria