I was scheduled for a 3-leg flight from my hometown to Dubrovnik (DBV). I made the booking through StudentUniverse as a single unit, and it appears that the 3 legs were all on one ticket, but they were on separate airlines. The first leg is on Jetblue Airways from my hometown to JFK. The second leg was from JFK to LGW, and I believe it was on Iberia. The last leg is on British Airways from LGW to DBV. The 2nd and 3rd legs had the same airline reservation code, but the first one is different. There is also a single "StudentUniverse Reservation Code" for the whole trip.
The issue is that the 2nd leg got cancelled. The substitute that I am being offered is also on Iberia, but it is scheduled to arrive at LHR at 6:50am. The 3rd leg departs from LGW at 11:25am, so I need to travel from LGW to LHR to make the connection. Is that enough time for me to disembark, get my checked baggage, go through immigration, take the shuttle to LGW, go through security there, and board my plane? It seems my best option for travelling between the two airports is the national express coach, which should be just over an hour of travel time.
Bonus question: I'm new to international travel, so is there anything I seem to be misunderstanding here, or is there anything else important about this process that I should be aware of?