Blackmail is a criminal offence so she could be prosecuted but that will involve everything coming out.
Ignoring the relationship side , you either continue to pay or you tell her that you do not intend to pay anymore and if she asks for any more money you will report her to the police for blackmail. Obviously you are taking the risk she will tell all.
If you intend to be with her I cannot see any problem with your wife knowing, she will have to find out sometime.
I cannot see you recovering anything if you sue the girl for money already given. She will say it was a gift and the court is unlikely to be sympathetic