Totally agree with Edge, use a compressor on Mic 1 that is controlled by Mic 2's signal. You should be able to silence Mic 1 when 2 is being spoken into, without much trouble. And will have learned an extremely valuable engineering technique at the same time
This is how the guy on the radio speaks over the music seemingly 'at will'.
If it doesn't happen all the time or there are times mic 1 AND 2 are active at the same time, you can use an envelope to disable (bypass) that compressor during those events and return it to use at will.