In addition to the really good litter box idea, you could fashion something to go around the piddle place or pad holder out of whatever material you have handy to add an edge.
You may also find some back-to-basics training helpful. Below is how I retrained my rescue dog who may or may not have had previous housetraining, but preferred to go outside.
My dog Gobo was trained to go outside when I got him this summer. I found it very helpful to put him in a small area with the pad/piddle place so he had to either be all the way on it, or partly on his bed. He never got his bed wet! I started with a 30" crate I had around, which was just big enough for a pee pad, a bed, and a water dish. I then moved him up to a pen about twice the size of the piddle place. Then to a 4' square pen. He had about 2 accidents when I took away the pen and he had run of the kitchen/dining room, but that was only because he associated the piddle place with the pen, which he didn't like.
First time Chihuahua owner with many years of dog experience!