How to use Reinhardt to fight hard AI in any non-payload style map?

Short Answer

Reinhardt isn't the only tank, there are other tanks that do non-payload map types well (see D.Va for Capture Points, Winston or Zarya for Control). Shake it up and try out a different tank!

However, since this question is specifically asking about Reinhardt, I'll also provide a Reinhardt specific answer.

Long Answer

Using Reinhardt when the enemy can come from more than one or two predictable locations comes down to placement of the Reinhardt. The easiest way to prevent getting flanked is to maneuver the map to your advantage. Stand near a corner or wall if on a control point, to force the AI to come at you from the frontal cone of vision. This works better vs AI due to the hero limits and the fact that tank shredders aren't AI-fitted yet (no Pharahs or Junkrats to ruin your day by knocking you about).

Once you're able to position yourself to force the enemy to come into your terrain, you can then dish out the hammer, scorch their faces or repurpose them as wallpaper at your convenience.

Cliff charging (a strategy where you charge a target off a cliff while distancing it so that your charge ends right at the edge) is arguably easier against bots as their movement pattern is more predictable once you're used to them. There are plenty of good maps where you can do this without too much risk of getting flanked while you're waiting for your mark.

Failing that, if you are able to communicate with your team- get them to cover your flank while you deny the main route of attack (the fastest path to the point etc). There are 5 other players in the game that can assist you if you're having trouble.