Okay, as for how she made it pop out - What if she parked right in front of the body in the first place? With the boxes covering the windows on one side, the kids might not have noticed as they got up close to it, and the wife was on the right side too so the teacher wouldn't have seen it either. The wife could have dragged out the body to that place earlier, and backed up in front of where the body was leaning by looking out of the window when they parked. (also, since she took the picture, she could have told them where to stand so they would block the bottom of the body which they might otherwise have seen under the car in the photo? or maybe she just lined up the body with the wheels) When she and Ayumi went to the front of the car, all she would've had to do is push the wheel of the car with her right arm when she was kneeling down and Ayumi wasn't looking, moving the car forward slightly and "revealing" the body. The dirt from the wheel would have rubbed off on the bottom of her right forearm. I think you can even see her doing it in a panel. Lmk if I missed something!
edit: also, in the panel where haibara is pointing at the body last chapter, you can see the two identical trees really
close to each other. the tree to the left was probably the once we saw in the picture. The proof for that is that the trees are differently spaced from the picture in the first panel of this chapter.