I also have a dog who is always on the wrong side of the door.
To keep from having to open the door for her every 5 minutes, I made her a doggy door in the screen door. For at least part of the year, she can be on whichever side of the door she wants.
When I first made this door, my budget was tiny, and this was a really inexpensive way to do it. I'm re-making the door (after 4 years, the flaps tore) and so I thought I'd write up instructions on how to do it.
Step 1: Supplies and Tools
Supplies* a slotted flat bar to support the flap
* 2' wide plastic carpet runner, two or three times the height you want the door; this is the flap
My carpet runner here is wider than 2', FYI
Make sure it's not one of the carpet runner strips with little spikes on the bottom
(I'm open to other suggestions, too)
* 5/16" pop rivets to secure the flap
* 5/16" washers to keep the rivets from just sliding through
* Barge cement (optional)
Tools* hacksaw or angle grinder to cut the slotted bar
* drill and 3/8" bit capable of drilling into the screen door
* eye protection for cutting/drillin
* pop rivet gun
* tape measure
* screwdriver (for manipulating screen cord)
* spring clamps (optional)
This was tremendously cheap, really. I bought all my supplies 4 years ago, but it shouldn't be more than $20 or so, I think.
It is possible to do all of this without taking the door down; I did it that way the first time. This time my back is much worse and I didn't want to spend that much time crouching, so I did it on a table instead.
Step 2: Measure
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Measure the height of the highest part of your dog from the ground. My tallest dog is 24" from the ground at the top of her head, but she still bumped into the door when it was 26" high. I'm making this incarnation 30".
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Measure up from the ground to the height of your door, and mark on both sides.
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Hold the slotted bar across at that height, and mark where the holes cross the height line.
Step 3: Making the Support and Opening
Put the bar across, lining up with the drilled holes, and use one rivet and one washer on each side to rivet the bar in place.
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Okay, screen is held in place with a little round cord pressed into a channel on the side. If you pull up the cord, you can pull the screen out. You want the edges and bottom below the support to be loose, all the way to the bottom of the support.
Cut most of the screen off neatly. Leave about 4" to wrap around the bar.
Fold the bottom edge of the screen around the bar, trying to make sure the part above the bar is taut. You may wish to use spring clamps or other means to hold the screen until things get attached.
You'll want to tuck the cord back in so it's nice and tidy, even though the bottom isn't securing screen any more.
Step 4: Cutting and Attaching the Flaps
I measured the distance from the bottom of the door to the top of the bar, and then added an inch. I cut two pieces of my carpet runner than length.
I had a chunk left, so I cut it in half to use as additional reinforcement.
Step 5: Attaching the Flaps
First I put the flaps approximately in place, then I overlapped the flaps to get the most coverage.
Then I folded the top of each flap across the top of the bar, so it would be attached in two places.
I used the Barge cement to glue the extra pieces of flap to the top for reinforcement.
Then I pierced the flap with an awl close to the edge of the door (to make a hole), put the rivet w/washer through the hole, put a washer on the far side, and used the pop rivet gun to attach it. This might have been a little easier with a spring clamp to hold it all together.
I did this on both right and left sides. Then I added a rivet in the middle. Then I added two more, one on each side. At that point it was well-secured.
Step 6: Cutting the Flaps Into Strips
I had wider flaps originally, but they seemed to be more stiff (and I think that's why they eventually tore). I'm hoping narrower strips will allow this incarnation of the doggy door to last longer. The first one last about 3 1/2 years, though, so not bad at all.