So sorry you are having this trouble. I know several folk who have had dogs who were going to have to be rehomed/destroyed but a good behaviourist was able to sort out the problem and the dog was able to stay, so please don't be too worried or discouraged. By getting advice as soon as you realised there is a serious problem, you are giving both dogs the best chance of a happy future.
As shoozie says, it is really important to make sure the behaviourist is qualified as there are lots of dodgy ones out there! Also, make sure you find one who uses positive/reward based training, rather than dominance or punishment training, which has been proven to CAUSE aggression in some cases.
You say they are both rescues - where did they come from? It might be worth contacting the rescue centre, although some can be more helpful than others! Also, many rescue centres have links with good behaviourists. Good luck with it.