Thanks for the reply! In terms of SES as a confounder, as we talked about in class, this is complicated because the direction of the causal arrow from SES to race/ethnicity does not make sense - so it is really more of a "third variable" whose treatment depends on what your research question is (e.g. do you want to know what the race/ethnicity association is independent of certain SES variables, acknowledging they are usually imperfect measures, or do you want to know the association of an outcome with race/ethnicity without controlling for the mediating effect of SES). Of course, most people just call it a confounder!
Also important to think about effect modification as a way of modeling SES.
I agree with the other comment that multilevel analysis, treating providers, clinics, or hospitals, is a common way to analyze health services issues like the one you are studying. As I talked about in the health care disparities lecture, this can help elucidate causes of disparities in health care - i.e. how much is intra- vs. inter- facility.