A discussion of the dynamics of a Banks’ Orbital can be found here (pdf)
http://www2.cmp.uea.ac.uk/~jrk/distribution/orbital.pdf
IIRC the dynamically stable point in a three-way is the Trojan point. (See how easily the double-entendres come when discussing heavenly bodies?) It was a key point in one of Asimov’s early short stories, the Trojan point is not stable when the two main bodies are too big, but for earth sun (or even for Jupiter-sun) the dynamic works. I suspect any other position would not be dynamically stable - you can’t put it in earth orbit, it’s too big and I bet the moon would disrupt any orbit. As with Ringworld, centring it on the earth would be unstable, even without dragging the moon into the equation. Anywhere else in earth’s orbit, earth would slowly drag it closer. It has to be approximately earth’s orbit to get the correct amount of sunlight and heat.