SPOILERS!!!
The secret to solving this mice problem is to have stable population of mice for several generations (I achieved this by feeding them as much as I could. Eventually there was population bubble, as more mice was born than that I was able to feed, leading to mass deaths and negative total happiness, but then population stabilized around about 80 mice), consequently accumulating lots of happiness. Then just suddenly stop feeding them and let them starve to death. It will decrease total happiness, but it will still be big and positive due to previous generations having happy life and dying from old age. This way you will get rid of mice, while causing them more good than harm.