It sounds like I am just one step ahead of you - learning serpentines as well.
The key with the serpentine is to remember to change your diagonals half-way across the ring. So...assuming you pick up the correct diagonal for the first curve, now you're headed back in the same direction you just came for the second curve, right? When you get to the middle of the ring - BEFORE - you look around the curve to start it - you sit for a stride and start posting again so you are now on the proper diagonal for the upcoming curve. I do a serpentine that has 3 curves to it (like an "S" with an extra turn at the bottom) and need to change diagonals 2 times during that process.
I think this is an important reason why we *do* serpentines - it's partly control of the horse at the trot, but it seems to be at least as much about ingraining the need to change diagonals when you change direction.