How far is it accurate to say that internal divisions within the trade union movement in USA was the most important obstacle to their progress from 1865-1992?
Internal divisions were partly responsible for the struggles of the American labor movement, but they were not the most important obstacle.
Internal divisions did matter. There were divisions between unions that wanted to fix capitalism and those that wanted to do away with capitalism. There were divisions between unions that wanted to represent all workers and those who wanted to represent only skilled workers. There were divisions between those who would have represented women and African Americans and those who would not. All of these divisions helped to weaken the labor movement.
But the biggest obstacle to unions was and is the general suspicion of unions in the American mind. Americans tend to believe more in the idea of individualism than in the idea of class solidarity. They tend to see unions as in some way anti-American because they represent a move away from the ideal of the individual worker making his or her own way in the world.
It is this distrust of unions, more than a lack of unity in the labor movement, that was and is an obstacle to labor power in the US.