Looking into this a touch further, I'll venture a few more guesses.
Erwin/Edwin/Edward Paulke Sr. married Edith "Edna" Johnson on 20 June 1928. She was obviously already pregnant with Whitey.
Whitey "Paulke" is born as Erwin/Edwin/Edward Paulke, Jr. on 21 October 1928, almost exactly 4 months after they were married. It does not appear that they had any further children.
From the biography above "when Whitey was 5, they moved" - I'd presume that Edna and her husband separated about this time, and she moved back in with her parents, along with Whitey - so this would have been around 1933-ish. For all I know, she began seeing Joe around this time, although there is no evidence to prove why she and Erwin/Edwin/Edward split up, or when she began to see Joe Ford.
Seeing the 1940 Census, it is interesting to note that Edna still has the last name of Paulke, is still noted as "married" and her son Erwin/Edwin/Edward is still carrying the last name of Paulke. Also, Joseph "Joe" Ford is in the home listed as a Boarder, but is noted as "single". Based on this, I don't think she had divorced her first husband by this time, but was separated 7 years or so by then, and probably seeing or treating Joe as her boyfriend/future husband.
The first date in Whitey's bio on Wikipedia is his signing with the Yankees in 1947. He would have been 19 years old. He would have also likely gone to one of their minor league farm teams (1947 - Butler (Pennsylvania) Yankees, 1948 - Norfolk (Virginia) Tars, 1949 - Binghamton (NY) Triplets ). But by 1950, he was playing for the New York Yankees in the Major Leagues, as well as the Kansas City Blues in the Minor Leagues.
So when we finally get to the 1950 Census, I wonder if he'll show up in New York or possibly Kansas City.