I don't have personal experience with this, but I've seen different (contradictory) recommendations:
- First, if necessary, there are anti-anxiety meds for dogs.
- I've heard you should let the dominant dog be dominant. Feed her FIRST, etc.
- I've heard that you should let NEITHER dog be dominant and present yourself as the alpha (I warned you it's contradictory

).
- You can do regular reward and correction sessions to help them get along. There have been a number of "It's Me or the Dog" eppys about dogs who didn't get along.
What did this trainer tell you? Do you think s/he was any good? Did s/he come well recommended? I don't think it would hurt to try another trainer if you aren't happy with the results of the first.
Finally, maybe it would be easier to re-home... I'm sure it would be painful, but perhaps that is the right decision. Both dogs could be queens in their own households.