Btw, the VO says Sahil said something about suicide again to Vedika and thats what seems to have made Vedika accept.
Vedika has already done bride swapping and what really has come out of it? Sahils been telling entire Kanpur that Vedika is his wife, is staying with her, claimed to be Arya's papa and Arya has accepted it too. He has openly rejected Nidhi and is hugging and kissing Vedika. Vedika herself has sat with Sahil as his patni in a pooja.
Sahil has been stuck to her much stronger than fevicol and no one is able to shake him off, least of all Vedika. So the only way to get him to run the business is by saying yes to him. Cause if people push him to stay away from Ved he is going to consider suicide and he has been very vocal about it to his family and Vedika. Inspite of all this if Vedika will still trick him, how really can she do that? If she back tracks he can always back track too and this time threaten her with suicide. Not a good thing to do, but given how much both Ved and his family have been pushing him... there is only so much he can fight when they keep forcing him to do their bidding. So Ved can come out with a really good idea or be married to him and try to show him how wrong they would be for each other, this might be a good track with the backdrop of Nidhi being the legal wifey, gives the added trp drama.
Finally after the fake preg drama and everything else Sadika would still be unshakable and it could be Veds realization. Eventually Sahil will shake Nidhi off and Vedika will become his legal wife. But that would take time. This would enable cvs go with their story line and also give us romance and help us go towards veds realization.