I own a pair of Capezio dance sneakers along with several pairs of ballroom and latin dance shoes. As the name implies, they are sneakers designed for jazz dancing. They have a split sole for flexability but the design still provides for good foot support. You should be able to find them at any dance supply store (ie. ballet, jazz, tap etc.)
I like them for social dancing, especially at venues where the floor is dirty (i.e. clubs). However, they are a bit too casual for wearing to semi-formal or formal dances. I don't like them for practicing for competition because they feel too different from my competition shoes.
On another note, there does seem to be some differences between brands of dance sneakers in terms of how they fit. I had to try on a couple of different brands before I found a pair that fit properly.
If you are going to have shoes custom made, I would recommend that you deal directly with the manufacturer rather than some distributor. My partner has had good luck dealing with Elegance Shoe Company from LA for custom made shoes.
Good Luck,
Blair