What you want is both a closer and a chain. The chain will prevent the door from blowing open too far, slamming the piston of the closer against the door-frame, and bending it. The chain should also have a spring to cushion the shock of having the door blow open to the limit of the chain, but that spring isn't enough to shut the door; you need a closer for that (covered in detail by lqlarry).
If the door can be reversed (and that's a big if) then I can't imagine it can be done without removing the entire door frame. The fixed pane is, well, fixed and unless you see a way to detach it from the frame and attach it to the other side then you may be out of luck.
So let's assume you can't remove the fixed frame. Well, you could try rotating the door. This should work, but it would put the rail on the outside of the door. I don't know how this exposure would affect the longevity of the product, and you'd certainly be prone to more things getting built up in the track. This also means that the exterior side of the glass would be facing the interior. A lot of modern glass has reflective coatings and treatments on the outside for energy efficiency purposes. You'd be losing this, and likely by making it worse in the summer (as energy would more readily penetrate and less readily escape).
Lastly, if your door is flashed and sealed, and if it has a flange around the frame, it might not even fit the other way without sticking out of the siding, and if it's vinyl it likely has drain holes in the frame which would now drain into the house.
You'd then have to reverse the lockset and handle on the door. This is probably the easiest part.
But, in conclusion, you should recognize that you would likely:
- Need to remove the entire frame from the opening
- Likely lose energy efficient properties from the glass treatment being reversed
- Expose your rail track to the exterior and additional wear
- Need to reverse your handle and lockset (and lose the ability to use the "bar in the track security method)
- Need to re-flash and re-seal the door (provided that there is a flange and that it's still usable)
In my humble opinion, each of these together would warrant simply buying a new sliding door to replace this one. Because the door frame isn't really all that expensive. The issue is the labor of removing, replacing and resealing the door.... which I think you'd have to do either way.
Best Answer
Your post says "screen door" but it sounds like you want to change the sliding glass door and the screen along with it. Most glass door units are modular, the glass sections (stationary and sliding) are separate pieces and the track runs the whole width of the unit. If this is the case it may be possible to switch things around.
Take a good look at the unit, the sliding door should lift up and inwards for removal. Once removed you may be able to see whether or not the stationary units can be removed. Look for screws on the inside and outside that are holding the units in place. The stationary units can usually be lifted up and removed as well. If we represent the original arrangement as A-B-C (with "B" being the sliding door) you might be able to replace them in this configuration: B-C-A.
The panels are heavy, don't try it alone. Prepare a flat area to lay down the sliding door so you can refurbish/lubricate the wheels while you have it off (I use sawhorses). Some old glass units are NOT tempered safety glass and could hurt you terribly if broken, be careful. The weatherstripping scheme, as well as the latch, may require some ingenuity as the setup will not be the same.
Not all glass door assemblies are made to take apart like described, especially custom stuff.