Ok I looked at how the door is constructed and it has a steel angle bracket going across the top and bottom a few inches from the edge. I thought maybe you could snake something up from the bottom but the angle bracket will stop you and I don't think you can get a clean shot at drilling through it.
I started operating the door handle and have some questions for you: Does you handle move like it is locked? Does it move like it is unlocked (you know what I'm talking about)? or is it something different?
If the door handle is broken - you know it is unlocked (even used the key to ensure it is) and still get no action but the door is latched closed, then these pics might help you.
This first 2 pic is from the center of the door looking down at the the bar that moves when you lift the handle. First is where it sits when door is latched closed
The next shows that the bar moves to the left when it releases the latch that holds the door closed.
This pic shows the left end of the door, this is the end that releases the door latch. I don't see any way to get to this but wanted you to see how it works. The cable you see in this pic is the other end of the cable that you saw above on the bar. The bolt sticking out toward you that you see the head of to the right, is there to give the mechanism a place to latch.
This a pic (sorry for the blur) shows that the cable is pulling down the metal that the bolt is mounted to and releases the door latches.
This pic shows the upper latch - when the door is closed the "U" is up - there is a matching one at the bottom of the door facing down. These doors are latched tight against the rubber gaskets mounted around the door frame
This pic shows the metal work of the latching mechanism and you can see it is behind that bolt, keeping it latched closed
This pic shows the "U" in the unlatched/open position
So you lift the handle, the bar attached to the handle mechanism moves left and the cable is pulled down, which releases the latching mechanism which forcefully pushes the door away from the frame and the springs lift it up the side of the coach.
Ok, so how do we bust into this thing? The only thing I can see is we need a way to move the bar to the left to release the door. I think that you need to drill a hole in the handle area to allow something in to get to the bar. Here is the handle from the outside. Notice the sloping bottom below left of the key and below the button you push for the "magic closing"
This is the handle area and mechanism from the rear. As you can see there isn't much room especially to the left of the bar - that is the key side. To the right of the bar you have more room AND you can see the sloping part of the handle area we talked about just above
Here is a closeup (sorry for the blur) and the wires you see to the right are the ones coming out of the "magic button". So my suggestion is you drill a hole in the sloping part of the handle about a 1/2" right of the button and toward the upper part of the slope
Drilling the hole 1/2" to the right of the button will bring you in to the "left" of the bar (as you're looking from the top). Looking at the pics you see you don't have much area to drill successfully through without hitting the mechanism. Maybe you could drill an inch to the right and come in behind the bar??? In this pic you can make out that there are nuts on the back of the bolts through the bar and you can make out that you don't have much room.
I am not sure what you can use to move the bar to the left and of course that will decide how big a hole you drill. If you need any more pics or a measurement I am happy to get them for you. You have other doors that you can investigate this approach on. I think if you do this right you won't be able to see the hole very easily and you'll patch it with something anyway.
Now if you answered the questions about the door handle acting a different way, then all this could be moot.