Looking for a Good Family Therapist

I don't have the name of a specific therapist for you, but I was struck by your framing of the problem and would encourage you to rethink it. You say that your kids are polar opposites. In what ways are your kids are polar opposites? This may or may not have anything to do with whether they get along. Where are you (and your co-parent(s), if any) in your self assessment? If you want meaningful family therapy it will require all of you to come to the table willing to own responsibility for some of the dysfunction in your family dynamic. Since you don't mention the dynamics between you and your kids, your kids and any co-parents, you and any co-parents, etc., it sounds like you want someone to serve as a referee for your kids' disagreements and "fix" your family dynamic that way.  What communication approaches are you modeling for your kids? Not what you are telling them is appropriate, but what is the actual practice in your home? 

And what are your expectations? Siblings bicker, siblings fight. Talk to other parents about their family dynamics; you may find that your kids are not at an extreme of the continuum. The reality of family life is that each individual affects everyone else. Your kids are not going to fit your platonic ideal of who they should be. Moreover, their ages mean they are at radically different points in their development; how does this magnify the problems? 

I gerw up with a sister three years younger than I. We had - have - very little in common. But that isn't why we didn't get along. This had other, deeper roots: favoritism, treating us as a unit rather than as individuals, and passive-aggressive relationship modeling, among other issues. Our mother mocked one of us and encouraged the other to participate. I didn't have the language to express how toxic the environment was, but it was, and to get away from it I figured out how to graduate from high school in the middle of 10th grade (with a diploma, not a GED) and moved to another city at the age of 16. I'm not suggesting that any of these dysfunctions are present in your family, but your family's dynamics are unlikely to improve if you can't identify the root causes and address them, and this will require that you evaluate your role in all of this.

Therapists are trained to react appropriately to their clients. Often this can mean listening impassively, but I urge you not to consider that the most important evaluative criteria in selecting a therapist. For some people that lack of response makes them feel unheard. 

It might make sense for you to look for individual therapy for yourself as well as family therapy. An individual therapist may be able to help you understand what you want to get out of family therapy. They may also be able to remind you that the goal of family therapy is to make things better for all of you, not just for you.

With two kids around that age (who actually have a lot of similarities which create incredible conflict), I feel like parenting teens is very, very hard. We have suggested family therapy as a quartet to one of them (tbh the one we see as more "provocative") and they scoffed. We do have sporadic sessions with their individual therapist (kid plus both parents), not the other child too, but they obviously are not committed to this and just waiting us out until we get tired of it and pull the plug. Waste of our time and money. The thing that is helping me the most is my individual therapist. Sorry to be long winded, and hopefully you get some recs for what you are looking for. If not... consider individual therapy for yourself since you are presumably a willing participant! That makes a big difference.