Do you mean this type of wonder bit?
If so, there isn't a western bit like this that is acceptable in the reining arena. I know that it can have shanks but cannot be a gag bit. I don't know whether a broken mouthpiece is acceptable or not. Most reiners use a ported curb bit similar to this for the show ring.
Here is what I copied off of the NRHA website, I don't know if they show you are looking at follows these rules or not.
Included in the infraction of abuse is the
use of illegal equipment. The NRHA Handbook specifies the
following as illegal equipment:
bits and snaffle bits with mechanical devices;
leveraged bits and snaffle bits having mouthpieces
constructed from anything other than smooth rounded material,
(Note: Twisted wire mouthpieces are illegal);
Leveraged bits with mouthpiece bar spaces less than
5/16” or greater than ¾” diameter;
nothing may protrude more than 1/8” below the
*bits with ports exceeding 3 ½” in height;
*snaffle bits with rings smaller than 2” or larger than
4” in diameter;
*snaffle bits with mouthpieces smaller than 5/16”,
measured 1” from the cheek. (Note: It should be noted that
a conventional snaffle can only be broken in one place. A
conventional snaffle may have loose rings. An optional curb
strap is acceptable provided it is loose, however curb chains
are not acceptable. No minimum or maximum width is required,
decorative knots and round material are acceptable.)
rope or leather bosals with wire, iron or mechanical
*bosal larger than 3/4” diameter on the cheek;
twisted curb chains or curb chains with barbs and/or
*wire on bits (Note: Spade bits may have wire wrap
on spacer bar only);
use of tack collars, tie downs, nose bands, electric
shocks, whips or bats;
use of any attachment which alters the movement of
or circulation of the tail.