I'm not getting the point of your question. I do have a 2 speed kickback coaster brake hub, but it's in an upright bike with horizontal dropouts and therefore bears virtually no resemblance to your application. A Catrike uses a circuitous chain routing and any I've seen up close had vertical dropouts necessitating a tensioner or derailleur at the rear wheel. This precludes use of a coaster brake for this application.
You need to give us more detail before anyone can address your question. Some photos of the drive train would help.Did the bike come from the factory with the coaster brake hub?