I think the 'conscious' Anandi wants to avoid messy legal hassles. As she herself said there is no point in doing all this because Jagya does not love her ... and proving the legality will not bring him back to her (she is only thinking from her perspective - not Gauri's) nor would she want a relationship where he is forced to be with her. In addition, she is concerned about haveli's ijjat.
The only benefit to anandi in declaring the legality would be to stake a claim on alimony, property, assets etc. And she knows she does not have to do it on legal grounds, Bhairon will automatically ensure that her future is taken care of.
To tell Gauri of legality is meaningless - because she wants Gauri and Jagya to have a happy life... and the legality of the marriage will only be important if anandi wants to challenge it, which she doesn't. So why go through the hassle of a divorce on paper?
The 'subconscious' Anandi may still not want to sever her marital ties with jagya, stupid as it seems after all that jagya has done to her. She may, in some secret corner of her heart, still feel that one day Gauri may fade out of the picture, and then if a and j marriage is still intact, then Jagya will come back to her. If they are divorced, he may go elsewhere. She said so herself that this is not my Jagya - it is some stranger Jagat from the city.
Personally, I think that as mahaan as anandi is being, there is still some subconscious revenge stuck in her mind, (not conscious, because consciously she wants to do the right thing) ...and she can always have the satisfaction of knowing that Gauri is just 'paraya' for Jagya.