For nearly 43 years, Francine Turner-Minor has distributed medicine to patients at a Baden neighborhood nursing home. On Martin Luther King Jr. Day, Turner-Minor went on strike from Hillside Manor Healthcare and Rehab Center, where about 130 elderly residents live, according to the latest count in federal data. Workers here say the facility is infested with bed bugs, mice and cockroaches, and they say they’ve faced union-busting tactics and unequal pay from the facility’s owners, New Jersey-based Luxor Healthcare. The concerns have become so dire that city leaders plan to investigate.