Okay, I have a few ideas; I hope at least one of them helps.
1. What do you mean by "the three children's whereabouts were unknown?" Were they old enough to be married and out of the house? If so, the pilot.familysearch website that someone else just recommended has some great marriage records for Michigan that cover this time period. If you're looking for daughters, that marriage info could lead you right to them. Perhaps the father moved in with one of his children after 1930.
2. This doesn't always work, but why not try looking through cemetery records online? You could try findagrave.com and/or the Michigan Tombstone Transcription Project.
3. Another thing that might help is to look for other surnames of neighbors and relatives by marriage. Look for patterns in residences, burial places, religion, etc. See if you can find documents or contacts for these individuals that could help guide you towards your family's information.
4. If your family is of Prussian/German origin, I can point you towards 2 or 3 cemeteries in Wayne County. If not, I'm sure you could still use information about their community to help track them down.
Good luck!
:) Mary E. Packard