A commentor on this post below noted--quite astutely I might add--that whether or not the The Bill Engvall Show was inspired by Sally Forth, the "pet/vacation" plot is quite honestly not the most original in the world.
In fact, I remember back in the 70's when sitcoms utiized what seemed like only a handful of possible plotlines, including:
* Long-quarreling characters get stuck in elevator/basement/shipping container and must work out their differences, only to come to both a mutual understanding and the same mutual dislike for one other.
* Neighbor's or boss's dog left in main character's care accidentally jumps off balcony and gets lost or killed, resulting in main character having to find a suitable replacement in time.
* Main character has to be in two places at once, usually at a big office meeting and a child's school recital.
* A conversation is overheard out of context and shenaningans result (otherwise known as the Three's Company device).
* Main character tries hard to impress the in-laws with disasterous results, only for their son or daughter to make a long-overdue impassioned plea about the worthiness of their spouse to their parents.
* The Harlem Globetrotters, Joe Namath or Sammy Davis Jr. appear.
Am I missing any?