Two separated itineraries mean that you will have to re-check your luggage. That means entering Dubai through passport control, pick up the luggage, go to check-in counter of Emirates and drop it off there while receiving your boarding pass to London. You will need to verify that you have the necessary documents to enter Dubai.
If you do not have the proper documentation to enter Dubai or your layover is extremely short that will not allow you to re-check your bags (entering the country, rechecking the bag, and re-entering security takes quite some time), change your tickets now. Don't get stuck in the situation when you arrive at the airport. Rwandair will probably not allow you to board the plane if you don't have the necessary documents to enter Dubai.
If you are able to re-check the bags but are just asking because "it's too much work", I would suggest just put up with it and re-check the bags. I do it all the time and it's not a lot of trouble.