The distance that your new portal needs to be away from the old one isn't terribly large, only 128 blocks, but it's measured in terms of the destination world; every block in the Nether is worth eight in the overworld, meaning you'll need to move around 1024 blocks or so away to keep a new portal from joining the one that already exists in the Nether.
I say "around 1024 blocks or so", because the existing portal on the nether side may already be some distance away from the location that would best match up with the existing Overworld portal.
There are, however, a few other options. You could try building a bridge across the lava on the Nether side. Painful and awkward, but once across, you could build a new Nether portal on that end, destroy the Nether-side one that exists (just punching it to turn it off should suffice), and hope that the new Nether-side portal successfully connects to your existing one. Alternatively, you might be able to make a suicide run through the portal, destroy the island so it's no longer a valid spot (and also destroy the portal on that side, too), then once you die and respawn on the Overworld side, a quick trip through should trigger the creation of a whole new Nether-side portal, which might not be in such a poor location.