Rulebook says that only cards attached to opponent’s Deeds/Dudes change their controller. There’s nothing about cards attached to Home/Outift. So Inner Struggle’s trait :
“While this card is booted, reduce your shootout hand rank by 1.
If you reveal an illegal draw hand and the owner of this card has a legal hand, boot this card.”
affects always only owner of this card?
Action • Cost 0
Condition
While this card is booted, reduce your shootout hand rank by 1.
If you reveal an illegal draw hand and the owner of this card has a legal hand, boot this card.
Cheatin’ Resolution: Attach this card to the cheatin’ player’s home, booted. That player discards one random card from their play hand.