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Gene Simmons and KISS turned down Donald Trump's invite to perform on Inauguration Day ... so says Gene's famous wife.

Poor Gene couldn't get a word in edgewise Wednesday night as he, wife Shannon Tweed and daughter Sophie left Catch in WeHo.

It's pretty clear ... Gene has warm feelings for Trump but there's a hard family divide, because Shannon and Sophie go nuts just hearing the Prez-elect's name.