Multiple Attack Penalty (MAP) applies to each Strike in the sequence they are performed in. Some abilities refer to this in words like
Apply your multiple attack penalty to the Strikes normally.
Note the words like "to the Strikes" plural and "normally", indicating the rules without an exception. That rule is
The second time you use an ...
No: Shoving or Grappling require an Attack action, not the Multiattack action.
SevenSidedDie's answer clearly explains why a creature must take the Attack Action to make a Grapple or a Shove attack and can not substitute one of the attacks granted by the Multiattack Action.
Moreover, the Sage Advice Compendium confirms SevenSidedDie's explanation:
Is the ...