How can I pitch a separate business existing within a business that is already existing?

My boyfriend and I would like to start a "coffee corner" in a trendy up-market general store in our small country town. We would provide all the equipment, stock and staffing, all the business would have to do is give us the bench space. We thought it would be good if we use their name for the espresso side of things, in this case it would "Name" & "Name" Espresso.

My questions before I pitch is: How much profit should I give them? Would that profit likely increase if we agree to use the store name? Does that give them any other legal ownership on the business because of that? Lastly: How do I ensure they don't take my proposal and just implement it themselves?

Thankyou!