It was advertised in Holy Temple of Mass Consumption issue #20, as found on a Usenet archive: REINCONATION 3. Radisson South, Bloomington MN; rms $63. GoH: Debbie Notkin; guests: TBA. Memb: $18 until 7/20/93, $25 after (children $7 until 7/20/93, $10 after). Info: Reinconation 3, P.O. Box 8297, Lake Street Station, Minneapolis, MN 55408. Guests of honor were Joan Vinge and Debbie Notkin (as also stated above). Geri Sullivan was publications head. Here's a short con report.
Eventually, we should have scans of at least the second progress report, program book and pocket program here.
An ad for ReinCONation 3 appeared in the Minicon 28 program book, page 5.
You might also be interested in the ReinCONation index page, used for ReinCONation 5, 6, and Not-A-ReinCONation.