Mia's feed

I really don't get it. If the mother had ipolito as a love child then that must mean that she was married to the cardinal and had affair with the man named Simon. Then why does having Arabella matters? No one except her would know who Arabella belong to so she could have just claimed her to be Simons as well and still run away with him...i don't get anything here. Is it the translation or is it the way the author intended? ╮( ̄▽ ̄)╭