You should get your coaster brake fixed, since it is apparently dangerous for you.

I have never had a coaster brake failure. Nor have I experienced a problem with engaging the coaster brake as you describe. I have always found the single coaster brake to be more than adequate and to be more reliable than any (set of) handbrake(s). I like the fact that I can skid the rear tire if I apply enough force. I live in a non-hilly area, so YMMV.