“Rush H. III has been selected as the name for a son, born to Mr. and Mrs. Rush H. Limbaugh Jr., 412 Sunset Boulevard, at 7:50 a.m. Friday at Southeast Missouri Hospital. The child is the first in the family and weighed 7 pounds 6 ounces. Mrs. Limbaugh was formerly Miss Mildred Armstrong, daughter of Mr. and Mrs. G. A. Armstrong of Kennett. Mr. Limbaugh is associated with his father in the law firm of Limbaugh & Limbaugh.”
From a Rush Limbaugh fan site. I can’t verify it, but I’m pretty sure Mildred worked at KBOA back in the early fifties.