The pedals don't spin backwards because the brake from the coaster brake conversion kit activates. The sprocket on the axle continues its forward motion even though the chain from the axle to the coaster brake locks as its to brake. From my experience with coaster brakes and cruiser, bmx bikes, is that when the coaster brake is applied, the rear wheel slows or locks depending on the amount of pressure applied when moving the pedals to a rear position.
On the trike, no matter how much pressure is applied to the coaster brake by pushing the pedals backwards, the rear axle and sprocket continue spinning forward. I'm not sure if the coaster brake conversion kit is defective or if the sprocket on the axle is a free wheel? When you spin the sprocket backwards it does make the traditional clicking sounds that a cassette makes. I see on some coaster brake conversion kits they come with a simple axle sprocket that doesn't have bearings and simply moves forward and backwards as the axle moves.
It has me puzzled, Sun bicycle has a 24T fixed sprocket for the axle which I was going to try but not sure how to even get the axle out as it appears to have been pressed in. As being part of the AZ community, I would hate to scrap the Sun rear assembly and then purchase a new trike conversation kit that comes with the coaster brake and rear axle, its expensive. I may need an easy fix but I just haven't been able to sort it out yet.