Low-metallicity really doesn't mean "metals", it means anything heavier than helium, IIRC. So it isn't necessarily that that there's less metal on a world, it is perhaps more like less solids to build worlds of. Similarly less metals might mean smaller metal core, which may or may not influence the crust. It is a problem with the classic metal-poor SF worlds, the authors may or may not rationalize what metal-poor really means.

However, from a purely stable view I'm not sure if the situation above would work -I wrote about moons a while back. If the planet is locked at a forty hour orbit and solar tides act to despin the double planet to such a degree it actually generates a really serious amount of tectonic heating I'd guess the planets may well be doomed. The energy comes from a falling moon, in a sense. How big is the second planet? Big enough to also be Earth-like?

If I'd do a metal-poor world in the "no industrial revolution"-sense I'd choose a situation with more dead tectonics. Huge highlands and mesas, erosional features (and thus less oxygen with dying cycles). So the deposits are largely covered by a lot of sediment (or ice caps). There's no serious mining not because of a lack of metals, but because of a lack of ore to easily dig up.