Normally don't like referencing wikipedia but I liked the opening sentence from the post about the Coping Saw (emphasis mine)
A coping saw is a type of hand saw used to cut intricate external shapes and interior cutouts in woodworking or carpentry
Still should have worked easier than you are describing though. Like Adam Zuckerman was asking the teeth count could play a role im this as well. Higher tooth count would have made for a cleaner cut. Sawing works best if you let the tool do the cutting and not use force. Also keep in mind that the coping saw is a push or pull tool. (Depends on blade orientation of course)
If you were making a dollhouse I would have expected lots of straight lines and edges. While a coping saw should be capable of doing that task I would not have thought it to be the ideal tool. Regular fine tooth hand saw would work for this if you have the piece clamped and immobilized as much as possible.
If I was going to use power tools I would look to bandsaw first for smaller projects or a fine tooth blade on a table saw. For a hand tool approach a smaller style bow saw would work but those tools are not readily available in stores. The bow saws you find in retail stores are more for cutting branches of trees.
Scroll saw would have similar issues with straight lines (without a fence of some sort) unless you are really good with one (I still need more practice).
I thought more about this and I wonder about the plywood quality as well. Cheaper plywoods will have the plies chip apart so they would tear more than cut. This would bind the coping saw making it harder to make fluid motions.