Regarding Child Custady Under Special Marriage Act

Hi , I am married to Hindu for about 10 plus years and we had a son 3 years back . From past 2 years she started acting cranky and started going out of town on office visits with one guy in her office which led me to suspicion and eventually she herself told me that she is in a relation with that guy in her office and she has got married to him but she has not clearly told me how . She just told me she got married to him in a temple once and later she told me they got married in a different country . She is still with me and we have moved out of India now but still these arguments keep going on and she still is in relation with that person and she still openly tells me she is married to him and she is with me coz of the kid and if we mutually agree for divorce and give child custody to her she will leave me . I don’t want to do that coz she has never taken care of the kid as a proper mother from the time he was born she just spends little money on him and spends a little time with him that’s it , the child has been always taken care by me and my wife’s parents till date . She keeps telling me that if we contest the case in court I will have no legal stand as in divorce cases always child’s custody goes to mother . Her grounds of other relationship and marriage is : 1) I can’t give secure life to her and kid because my earnings are low and I have not saved money 2) My family members never accepted her as she is Hindu and she did not get that recognition 3) I don’t do things on time as she says and I am lazy 4) I did not write the property in her name because I don’t want to where as other brother of mine has written properties in thier wife’s names 5 ) I am overweight and in spite of she telling me so many times I did not reduce My points 1 ) she had done similar thing once before with another guy in the same office but it did not go to the level of marriage. She use to often go out of town with him saying it’s office work and once I had also cought her when she had gone with him to Goa . 2 ) she use to bring expensive gifts from that guy then after 2 yrs somehow that relation got stopped and that guy got married to some one else . 3) she started this another relation with a guy in same office who was in senior position and started doing same things initially started going out saying office work then started bringing expensive gifts 4) eventually just like that got married to him with even telling anybody or legally divorcing me . I want to know what my legal stand is if I contest for child custody .