Where is your water softener located? Isn't it anywhere near a drain with a trap in it, such as your washing machine discharge standpipe or a utility sink? Traps are what keep sewer gas from entering a home. I highly doubt that a dishwasher air gap will work for that.
Black plastic drain pipe is ABS, not PVC (different "glue" requirements).
Please give us a little more detail about what you're working with (layout and rough distances), and we'll try to help. (BTW, I am not a pro plumber, just a long-time DIYer, but there are a lot of pro plumbers here who can help you.)