According to Nixon's still-living daughter, Patricia Nixon Cox: "Because I lived at home with them and my sister, I can state unconditionally that at no time during 1962 or ever did my father ever strike my mother or did my mother ever have physical signs or bruises of the type claimed in this book." She also said that "these claims are based on statements attributed to two persons no longer alive, by a man [retired Washington lawyer John Sears] who did not meet either of my parents until years after 1962."
In other words, this claim -- while certainly believable about a man of Richard Nixon's character -- is just plain unsupported. The most reliable source of evidence says it just didn't happen, and the only sources saying it did are guilty of hearsay.