So first, you need to decide who has priority if suppose BOTH players try to move the sprite at the same time? Where would it go? Let's assume Host has the priority.
If Host has synced the object, and Peer can see it.
Then let Peer send Touch.X, Touch.Y to Host
Store it in an some global or instance variable, peerX and peerY
Now: if Host touching object: Sprite set position Touch.X, Touch.Y
Else: if Peer touching object: Sprite set position peerX, peerY
How will you know if Peer is touching object? and stop touching? You can send some boolean (or number) from Peer to Host (as Message) to tell Host "isTouching" and "stopTouching".