If you have credible evidence that your father have committed adultery then show him that you have committed adultery therefore my mother is bound by your act to take divorce and she is ready to file divorce petition because she has strong evidence against you.
then read your father's expression or conduct. if he is trying to settle this issue then you can do so. you should borne in mind the legal precedent regarding woman's right of alimony.
1. right of alimony under section 125 cr.p.c. [ no need to file divorce, adultery is sufficient cause for wife to live separately on the alimony from husband]
2. alimony under Protection of Women from Domestic Violence Act, 2005 [ no need to file divorce ]
3. file divorce on the ground of adultery
judgments:-
1. Vinny Parmar vs Paramvir Parmar [2011] : amount of maintenance fixed for the wife should be such as she can live in reasonable comfort considering her status and mode of life she was used to live when she lived with her husband.
2. In Chaturbhuj vs. Sita Bai [2008] : the personal income of the wife is insufficient she can claim maintenance under Section 125 CrPC.
3. In Bhagwan Dutt v. Kamla Devi : wife should be in a position to maintain a standard of living which is neither luxurious nor penurious but what is consistent with status of a family.
4. V. Tulasamma & Ors vs V. Sesha Reddi : It is well settled that under the Hindu Law the husband has got a personal obligation to maintain his wife and if he is possessed of properties then his wife is entitled as of right to be maintained out of such properties. The claim of a Hindu widow to be main- tained is not an empty formality which is to be exercised as a matter of concession or indulgence, grace or gratis or generosity but is a valuable spiritual and moral right which flows from the spiritual and temporal relationship of the husband an wife. wife has right to claim her share in the husband's property.