Option A. Don't even use the mouse over condition on the peer end. Let the host decide if the mouse was over the object or not.
Option B. Don't worry about keeping drag and drop host authoritative and synced. Basically favor local input prediction and responsiveness over host authority, and have the host and other peers catch up to the current peer location instead.
There is no way to remove latency in the real world. You just have to design around it, weather you decide to favor host authority or local authority is up to you. Designing netcode is all about how to best hide the latency from each party involved while preventing inconsistencies and conflicts.