...is that Frodo did not use the power of the Ring to dominate Gollum.
Tolkien explicitly says that his heightened strength of will was primarily
directed toward his own resistance of the Ring. And though he clearly did
dominate Gollum to some extent, there's a world of difference between doing so
on an ordinary level -- even using threats, such as they were -- and using the
actual power of the Ring to do so. There's no evidence that Frodo did
that; indeed, I think if he HAD tried to use the Ring that way, things would
have gone much more badly for him much sooner. Remember, Galadriel told
him that he would need many years of training his will to the domination of
others in order to use the power of the Ring, and if he tried without that
ability, it would break him. (Which is another reason I don't believe
Frodo made use of the Ring in that way.)
What he used it for was the carrot to keep Gollum in line. He knew of
Gollum's desire and need for it, and knew that so long as he held it, he COULD
dominate Gollum enough to make him useful to them. But I also believe it
was his pity and kindness toward Gollum that prevented him from attempting to
slit Frodo's throat while he and Sam slept; the Ring could not have elicited
the gentler feelings of affection from someone like Gollum. That was
Frodo's doing, without the power of the Ring.
And there's that scene on Mount Doom to think about: "A crouching shape,
scarcely more than the shadow of a living thing, a creature now wholly ruined
and defeated, yet filled with a hideous lust and rage; and before it stood
stern, untouchable now by pity, a figure robed in white, but at its breast it
held a wheel of fire."
Given Tolkien's usual symbology and imagery, if Frodo had been using the actual
power of the Ring, I doubt very much he would have appeared as "untouchable by
pity, a figure robed in white." The image of Gollum is one corrupted and
wasted by the Ring, yet though Frodo holds the "wheel of fire," he is still not
stained by it, not in that way. He has used the fact that he has it and
that Gollum wants it to dominate him enough to make him obedient, yet until the
very end, when he reached the limits of his ability to resist the pressure of
the Ring, I do not believe he ever attempted to use its actual power to force
his will upon
Gollum.