..between the power and influence of the Ring and the power of the one who
wears and wields it.
The examples you give are of those who have at one time been Ringbearers. I
think anyone who possesses the Ring even for a short time is susceptible to its
influence. The Ring apparently begins claiming its bearer almost instantly. And
forever after that, they are bound to it in some way; it makes a slave of them
in proportion to the length of time they held it and the use they make of it.
Bilbo held it and wore it. He cannot come near to it without being affected.
Gollum held it and wore it so long and so often that he was never free of its
effect and power over him. He sought it across ME. Sam held it and wore it very
briefly, but he still felt the pull and the beginnings of the terrible jealousy
of the Ringbearer.
This is the power of the Ring over its Bearers - it does not need another to
exert the power of the Ring to cause it; the Ring needs only to exist.
But for the Ringbearer to control (I think the most accurate word would be
enslave) another being, he must use the power of the Ring, and direct it toward
that person. In order to do so, the Bearer must claim the Ring as his own and
strive to direct its power toward the person in question.
I don't think Frodo ever exerted the power of the Ring, until the very end -
and then, it was to challenge Sauron. He merely threatened to use the bond that
already existed between the Ring and Gollum. Gollum's good behavior was
guaranteed because he chose to give obedience and still retain some small
amount of independence. If Frodo had actually used the Ring, I think Gollum
would have been entirely enslaved, and would no longer have been able to resist
or betray the commands of the Ringbearer. But I also think it would have
required Frodo to exert it continually; I don't think he could have used it
without exhausting his will entirely.
As has been pointed out, Gollum's promise was to the Precious itself, not the
Bearer of the Precious. It was that fact that allowed Gollum to plot with
Shelob. If he had sworn to Frodo, he would not have been able to betray him. As
Frodo warns him, that vow is treacherous - the Ring is not
trustworthy.
Silverlode
"They looked as he pointed, and before them they could see the stream leaping down to the trough of the valley, and then running on and away into the lower lands, until it was lost in a golden haze."
