Dahlgren, according to a book written by his grandson Matt Dahlgren, was traded away by the Yankees because of suspicions that he smoked marijuana. Yankees manager Joe McCarthy is fingered as one of the perpetrators of the rumor and was instrumental in getting Dahlgren traded after the 1940 season.
Eventually in 1943, Dahlgren decided to undergo a drug test and medical examination, to clear him of the charges.
Dahlgren moved around a lot after leaving the Yankees did move around a lot as you can see from his B-R entry. After Gehrig, the Yankees first basemen were not an overly impressive bunch until Don Mattingly came around.