Answer
Look for a state-type field already present in the shared underlying view/table that distinguishes the two scenarios (for example, a STATE field that's one value for a quotation and another for an acknowledgement) — you can reference that field to dynamically select which layout applies. Set this up on the Report Rule page: create an action there and specify which layout to use based on that condition, which lets a single Print button resolve to the correct layout automatically instead of prompting the user to choose.