Maxperson
Morkus from Orkus
Here is an interesting comparison:
Two fighters. "Shield Master" Sam is a sword and board with Shield Master. "Two-Weapon Fighting" Todd is a Dual-Wielding sword savant (with Two-Weapon Fighting Style). Both are Level 5.
Sam can attack, attack, shove;
Todd can shove, attack, attack.
Sam's breakdown. Attack action (sword) with Extra Attack (sword) and then bonus action to Shove.
Todd's breakdown: Attack action to Shove (as "special melee attack" using one of his attacks from the attack action), Extra attack (sword), and then bonus action (sword) from TWF.
Both have two attacks, both can shove.
However, Todd could never shove last since his bonus action comes after completing his Attack action, and TWF only allows you "to attack with a different light melee weapon that you're holding in the other hand." In other words, it has to be a weapon attack, not the "special melee attack" of the shove action.
Does that bother anyone else? One can only shove last, the other can only shove first. Why? It seems a silly distinction to me.
Todd can shove last if he wants. This is the two-weapon fighting rule, "When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand."
The bonus action doesn't have to be used immediately, so assuming Todd has extra attack, he can attack, shove, bonus action attack. Or attack, bonus action attack, shove. Or shove, attack, bonus action attack.