that buying two returns thing is called a back to back ticket and it is a big no-no, if the airline catches you they will cancel both itineraries and debit the travel agency that issued it big time. basically, back when the airlines required a saturday night stay for their cheapest fares, people who basically wanted to make a two day round trip, such as business travelers, and who didn't want to have to pay a thousand bucks for their ticket, would simply buy, for instance, one round trip JFK
for Monday to Sunday and a second round trip SFO
for tuesday to the following monday, for say 200 dollars each, then they'd get on the plane on monday, basically throw away the return, do their business, and get on the "return" on tuesday, again throwing away the return portion of that ticket and thus they got 1000 dollars worth of air travel for 400 dollars, as long as their plans didn't change. if you're on a back to back ticket and you suddenly find that your boss wants you to stay until wednesday, and you try and change that ticket you're supposed to travel on on tuesday, you're changing your outbound and that entire ticket gets prepriced, talk about expensive! in my line of work i've dealt with exactly that scenario and it's not comfortable from my point of view to have to explain that that ticket they thought of as their "return" was considered to be the outbound by the airline and thus was considered unchageable. and they will argue all day long that the second ticket is their return and why can't it be changed for just the change fee? all i can do is explain that as far as their airline is concerned that second ticket is their outbound and when you change the outbound on a nonrefundable ticket, the entire ticket is repriced to today's rate, and furthermore, most airlines won't allow you to apply a nonrefundable ticket towards a refundable one, so not only do you have a ticket you can't really use, but you have to pay 1500 dollars for the ticket you need to get home.
long story short, don't try to do a back to back, you won't get away with it.
as for the whole stopover thing, my suggestion would be, if you have a ticket from LHR
with a stopover, and you decide once you're in new york, you want to go to miami, do it as a separate ticket, because if you do it on the same ticket, it's going to be considered a routing change and the rest of your ticket will be repriced.