The emperor lust over the mother, but the mother has little political backing, so he married the empress.
Then he put the mistress to marry the marquiss with a mine as the dowry.
Mother birthed to Tia in order to have legal right to the marquis's line, money and all, so she has money to support his son in his pursuit of the throne. She abused Tia in order to make Tia relied on them.
Now her children choose to back away from her. She reaped what she sowed.