husband and I always screened potential therapists before having our kids meet them to see if it might be a good fit. We then told the difficult child (whichever one it was) that he needed to meet the therapist and give it a few times before deciding if he would continue. We hoped the therapist would have a good way of reeling the difficult child in. For example, difficult child 1 likes baseball and computers. One therapist we used for a while played catch with difficult child 1. His current therapist has played computer games with him on occasion. In the context of "play," the therapist and difficult child 1 talk about issues.
When interviewing potential therapists, find out their training and background, if they have experience working with kids like your difficult child, how they would approach your difficult child (with play, cognitive behavioral therapy, psychotherapy, etc). You also might give some info on your difficult child's interests so the therapist can have some idea of how to relate to him.