I responded to this but did not read your question properly. Whoops.
Is the free Prime with Amazon Mom only for if you are not a current Prime member, or can you cancel Prime and get it for a year for free via Amazon Mom? I'd find out for sure since that's $80.
We only used Amazon Mom for the Prime (and we are paid Prime members now)... we use a mix of cloth and disposables but always got our disposables elsewhere.