Being a smart woman, noble, and rather wealthy.
Young or old Tywin would marry you for your statis not because he needs heirs but because he'd either need a strong army or gold.
You'd be witty to the point where you'd sware you'd see him smirk trying to hold back his pride at having a wife such as yourself.
Being escorted everywhere by at least two Lannister guards at all time, sometimes four just so Tywin would know you'd be safe.
Going where he'd go rather it be Casterly Rock or King's Landing. He'd want you close, excluding the battle field.
Seeing the side of him that rarely any others see, so long as he wasn't disappointed in you like his children.
Often at times contributing to the family, knowing that he holds his lineage above all else therefore helping him to guide his family in the right direction as best you could.
Being the ruler at home. Tywin would undoubtedly leave things such as the minor tasks of upkeep for Casterly Rock in your hands since he has more important matters such as being Hand of the King.
Never being disrespected by anyone so long as Tywin is alive. Feeling just what true power is whenever you walk beside him into a room filled with people.