How come Earth has two Stargates, and why does one of them get "priority"?
In essence one wormhole from one planet can be established. Only one address exists, one point of origin. The first one to receive the connect signal gets activated, which is why the Antarctica stargate gets the signal and the SGC gate does not.
Also, the Antarctic gate had a proper DHD and the SGC had a home-grown dialing computer. The ancient system must prefer its dial device over a non-standard one, and will also prefer any stargate linked to a DHD vs. a stargate without one.
Earth has two stargates, the one Ra brought with him, and the one the Atlantians (Ancients) created on earth.
Also, Earth having 2 stargates is answered here:
According to the Stargate Wiki, the gate using this symbol as the point of origin was brought by Ra from an unknown location. This gate became the gate used by the SGC. The point of origin on the gate found in Antarctica ("Solitudes", S01E17, now known as the "Beta gate") is the original Lantean-specified one.
The Antarctic gate was Earth's original stargate, which was buried in the antarctic ice.
Ra brought the other, as Justin said.
Priority to a gate is driven firstly by the presence of a connected DHD - A gate with the original DHD gets priority, so long as it is valid.
It seems that the presence of ANY DHD (including homegrown versions, like the SGC's) gives a gate priority over one without a DHD, though the method of detection is unclear.
For reference, see the Episode 'Watergate', where the Russians operated their own gate program (briefly), connecting a DHD to get priority when a team was due to return. At other times, the DHD was disconnected, allowing SGC's gate priority.
Due to only one Gate being able to be opened and sending a matter stream at one time the open gate will take priority over the other. Also, the Antarctica Gate had a DHD (Dialing Device) with it. This device provides faster dialing times and priority over the gate in the SG-1 base which is jury-rigged with human computers and other tools.