Firslty, as you have stated that you want to settle it out side the court which is somewhere I think a right thought that you have got.
Secondly, but, before that, you may have to get one thing clear as she has made her mind that is why sent you that notice, so the option which you are thinking to use may not work.
Thirdly, I advice you to file divorce petition on the ground of mental cruelity as she says you have extra marital affair which is not true at all.
Fourthly, if she files divorce before you file it then thereafter things will be changed if she files any criminal complaint against you or family members.
Fifthly, so, you please think and then decide, if you wish, you can avail my services through Kaanoon.