In this past year’s Yale supplement to the Common App, they ask whether any of your grandparents attended Yale University (they will get any parental affiliation from the Common App section asking about parental background) and they ask if any relatives have worked for Yale University. They wouldn’t ask for this information unless it somehow factored in the process. So, your mom’s affiliation would be a plus. However, I suspect there are different levels of pluses. Being a child of a tenured professor or senior administrator is probably going to carry more weight than being a child of someone who works at the hospital. I also don’t think being a “fellow” of a residential college carries significant weight unless the fellow is a known and active contributor to the college to the extent that someone like the Master/Head/Dean of Saybrook is willing to be an advocate with the AO. Bottom line, the success of your application will depend on the factors that all candidates will be judged on. Your affiliation would be a small (probably very small) plus. Good luck next year!