So part of the problem I have with that is that it turns the counselor into a judge, weighing in on the wants or needs of the parties, and delivering with weighty authority the verdict about who is right and wrong (or even worse brow-beating one party into agreeing with the other). We'd never let a lawyer represent both sides in a transaction, why do we let counselors? At least with mediators there is an understanding that it won't be a "right" position and a "wrong" one, only a mediated one. There is no correct answer on most of this, only people's positions, perceptions, and yes, the dreaded feelings. (So perhaps find a mediator trained as a marital counselor or a counselor who specializes in mediation).
If someone thinks the kids from a first marriage should come first or even on the same plane as subsequently born children, that is his position, and a reasonable one. If he isn't sure and can't get there through self-reflection, or doesn't feel strong enough to self-advocate, then maybe individual counseling could be helpful in problem solving and self-advocacy (but the internal resolution should still be his own). I think we forget how little training these folks actually get and that most of them try to hold themselves out as specialists in every possible issue (read some of their profiles on psychology today if you doubt me). Every case is different and trying to bring together two people already in conflict would take the most skilled person imaginable. While I'm sure such a person exists, most are never lucky enough to find them. Even Gottman has been married more than once.