The place where it is most apparent that the "addition" was once a porch was the interior wall in the animal room where they never bothered to cover the old window and left the stucco wall
How ugly and stupid. We knew this weird wall had to match the rest of the room so we set out to cover the window and retexture the wall so it didn't look like stucco anymore.
First up was insulation
Then we furred out the wall to build it out as much as possible so that the new drywall surface would be even with the stucco surface
Next came installing the drywall. We only had green (purple) board laying around, but we figured what the hell and threw it up there anyway
Chris researched a bit online for a product he could apply on top of the stucco that would allow him to retexture it instead of going through the awful and messy task of ripping it all down and laying drywall. The wall was strong enough and there weren't any problems with it, we just didn't like the texture. So he found out that if you apply plaster-weld to the walls it provides a surface that joint compound can fix to without cracking or anything. It's normally pretty expensive, but Chris found a good deal and bought a bucket o' plaster-weld and got to work painting it on
Once the plaster-weld was applied, it was time to apply the joint compound in thin layers until the stucco texture was no longer visible and then applying our texture to the walls
Certainly a vast improvement from a wall that had a hole for a window and visible stucco.