Was this the DL2004/ DL4638 connection? That is scheduled to arrive SLC at 19:29 with a connection outbound to OKC at 20:05. 36 minutes. And on June 22, it arrived about 30 minutes late.

If this was your booking, you made a significant gamble with such a tight connection. It can be done (I will do so if travelling alone on urgent business, but only if there is a later departure on the same day where my status may have some pull to get me on standby).

Best approach, especially with family in tow, is to have at least one hour at each layover point, and also best not to rely on the last flight of any given evening.