You can only have one Ship or Base mining in a sector, period. Or, you can have sats. With satellites, you can only have 3 operate, one mining each type of resource. Extra satellites will not produce any more resources. Having a base and satellites will result in either the base or the satellites mining, depending on which was built first and some random absurdity.
Ie: it sometimes has the first built object mine, other times has the Last built one mine. I noticed this when replacing Space Stations with Battlestations in Proportions games.