Rizpah's Sackcloth will discard cards in both the side battle and the main battle. However, the G Deck Deceit of Sapphira ("Discard all cards in battle (including yours). Cannot be prevented by an evil card.") will only affect the side battle if it's played in the side battle.
REQ, Definition of Battle:
"The phrase ‘in battle’ or ‘current battle’ refers to any cards in the current battle that can be either the primary battle (rescue attempt or battle challenge) or it can refer to a side battle, NOT BOTH."
"The phrase ‘Field of Battle’ refers to any cards in the Field of Battle including primary battle and side battles. Example: Deceit of Sapphira* and Rizpah’s Sackcloth both read, 'Discard all cards in the Field of Battle including yours.' Either of these cards will discard every card in the primary battle and the side battles regardless of which battle they were activated."
*The Women of the Bible version has the listed special ability, and is different from the G Deck one above.
