Adjusting for confounders in economic conditions

This is my first question on this forum. I am studying a condition that is common in early childhood. I am analyzing nationwide data. My hypothesis is that the condition is more common in children living in poorer neighborhoods than those living in richer neighborhoods. The economic condition of children are divided into four groups(order) : 1, 2, 3 and 4. Other variables that are important are race( white, black, hispanics, others) and geographical region(northeast, midwest, south and west).
Until now, for these analyses, I do univariable logistic regression with economic condition followed by checking for mediation, where I add race to the logistic regression, to see if adding race would change the impact of socioeconomic condition, as race is a potentially confounding factor. I am doing it right? Or what would be the ideal way figuring out if economic condition has an impact on this childhood condition while taking into the impact of race, geographical location and other potential confounders?

By dichotimizing economic conditions in only 4 categories you likely have unmeasured confounding related to economic conditions. When you add race, you might be accounting for some of that unmeasured confounding. Is there a reason to believe that race relates to the condition you are studying? Sometimes people will model an interaction between economic conditions and race because they may be differentially disadvantaged.

Thank you for your input.
There is not much in literature about the influence of race on this condition. The condition is more common in Black and Hispanic than White. The differences in race could be due to impact of economic condition on race. I will check for an interaction between economic condition and race.