I'm going to show you what I did and tell you what I will do differently in the future.
First, I made the pattern into one piece. You can still sew the panties with the different pieces, but you need a single piece to make the pattern for the inside.
Next I traced the inside and across for a lining piece.
I made a shorter version for the absorbent insert.
I cut the insert out of an old newborn diaper. You could also use a towel. The first thing I learned was that using a non stretchy insert is greatly going to reduce the flexibility and overall size of your finished panties. This is going to turn your panties into a size or two smaller than the initial size you cut. I would suggest using two t-shirt layers with the stretch across so that it doesn't do this. A diaper or towel might be your best choice for a baby or toddler that you are just starting to train, but if you are making training pants for a child that gets it but just isn't perfect, I would definitely go with the layers of t-shirt.
I cut the other two pieces out of the knit. This is an incredibly cheap knit that I suspect is a poly/cotton mix that I inherited from my MIL. I suspect that the panties I make out of this are not going to last through many washes.
I serged the insert to the lining across the back.
Then, I serged the back to the front as normal. I topstitched the panties with a zigzag on the front and the back where the lining is.
If you have a thin child or potty train your child very young, making your own is definitely the way to go. The smallest training pants that I have found for purchase is 18 months (we have the Gerber and the TRU brands) and even after sewing them down the sides so they are 2 inches smaller, the bear cub often has to pull them up when they fall to her knees. These are definitely going to stay put better. The bear cub loves the polka dots and kept pointing to them. I think she'll rather enjoy picking out her own fabric, too.