Here is a picture of the lining of the training pants with cotton batting sewn to it. These tp's have one solid layer of batting that goes from the front to the back and one layer just for the middle. This is suggested for girl undies. You can add the extra layer to the front for boys undies, or use just one layer.
The tip I have shared with others with this question is to try just printing the whole pattern at about 80% instead of 100% (you can adjust it in Adobe reader, or use a copy machine). You can also cut the binding that goes around the leg and waist holes a bit shorter so that you have to stretch it more as you sew it on, and that will make them more snug- and of course make the waist elastic smaller.