I had red wine spilt all over my new white jeans when I was in Hollywood. I couldn't clean it for another couple of days until I got home. I thought for sure my jeans were DOA.
When I got home I took my bleach (Javex with fibre guard or something like that, it doesn't hurt the fabric) and used a spoon and poured it on top of all the stains. I saw the stains disappear within 10 minutes. It turns purple around the outer edges of where the bleach ends but that washes out in the wash. Then I threw it in the washing machine.
Was your jacket dry clean only? I sometimes wash my dry clean only items in the washing machine under the hand wash cycle in cold water and hang them to dry.
If the dry cleaners can't get the stains out, then try what I did.
p.s. don't wear your nice clothes when trying to bleach. I learned that the hard way.