I'll make an assumtion here that the throw did not beat the batter/runner to first. If that was the case the lead runner would be out, when tagged, or the runner entitled to the bag is safe which is the batter/runner. In this case R1 was forced to advance and is no longer entitled to first. With that said, had the throw to first beat the batter/runner and she was out, then R1 was no longer forced and can remain on first.
It is not always the lead runner that is out when two players occupy the same bag. The runner that is entitled to the base would be safe and the other runner, when tagged is out. If the lead runner is not forced to advance, then the trailing runner is out when tagged.
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