I feel in the confused state of affairs the Endgame is going to be Naira herself giving Kairav's custody to Karthik because she would have some fatal disease (for the track only) and would leave for Goa with the permission of Singhaniyas. And Karthik would stop her.
I guess however boring and lame it sounds, Vedika and Karthik are faking their marriage not only to Naira but to the whole family also.
May be Vedika promised Karthik to help him but then she double cross Karthik and started emotionally blackmailing Naira, in order to win the game by hook or crook!
And logic no more works in Yeh Rishta as it's on Ekta mode.