First of all ascertain whether the kids are yours or are of someone which even she does not know. 

If they are not yours then lodge a complaint in the police station for blackmailing and taking money and ruining your family life.

If the police do not respond then file a complaint case against her before a magistrate and he will direct the police to investigate the matter.

Regards 

I would suggest you not to escalate this by reporting it to the Police.

Settling this out of Court, is the best way open for you.

You have a lot at stake in comparison to her and hence, if she is ready for compromise in lieu of payment of one time settlement amount, it is better to close this for once and all. 

Out of court settlement for what? That particular lawyer has misguided you. 

1) first of all you need not be scared of any criminal prosecution against you, as you indulged in consensual sex with an adult female. 

2) Your wife too cannot prosecute you criminally, as you didn't commit an offence of bigamy. 

3) The only thing your wife can do, us seek divorce in family Court. It's a civil matter and doesn't involve punishment. She may seek alimony. 

4) That bar girl has no legal right to seek maintenance . 

5) Now for the twins... Well yes you will be responsible for their maintenance, but for that, they have to establish that they are your twins, by way of paternity test (DNA test) 

6) So the bottom line is, you need not be coerced into going for any settlement with the bar girl. 

1) Dance bar is not allowed in the state and you will punish for bigamy act. If the twins are yours than need to prove by the of doing DNA test you will come to know whose are the twins than.

2)Till that time stop giving her money and get done first DNA test. After doing dna test than come to compromise or settlement later.

1) DNA test would reveal who is the father of child 

2) if you are not the father you don’t have to pay any maintenance for the twins 

3) in case girl files application for manintenance you should contest the proceedings . If DNA tests are negative take defence that you are not father of children and not liable to pay maintenance 

See you can file a police complaint against her for intimidation.

In case they are your twins they can seek maintenance from you.

Yes if out of court settlement is possible go with same and make an MOU for same.

Better settle the matter out of  court through an mediator or advocate and execute a MOU. 

For settlement she will demand more money. Let her file any case. You can file case of blackmailing threatening etc against her.dont succumb to her pressure she has already revealed it to your wife. It may not be your kids.

No punishment as no criminal offence but liable to maintain them.

Get the DNA done to verify if they are your daughters. If it is proved, not your child , You are free .

1. If the twins are indeed your flesh and blood then their mother can seek maintenance for and on their behalf from you by filing a DV case.

2. To stop this girl from coming to your house again the only remedy in your hands is to file a suit for permanent injunction in the competent civil court.

3. Out of court settlement would be best solution in this scenario.

Dear  Sir,

- Legal battle will be too long.

- Advisable to settle out of court 

- However incase you wish to proceed with legal battle,collect as many as evidence against the statement before proceeding.

Regards

Vivek Arya

If there is a possibility to settle the matter out of court with a reasonable amount, you may better utilise the opportunity.

If she claims that the twin children are yours, ask her to prove it before court by a DNA test and after that you can pay maintenance to the children because she is not your married wife hence she may not be entitled for any maintenance.

If she is taking up the issue legally, she may not be able to achieve anything with the given nature of her profession.

1. As per the information mentioned in the presnet query, makes it clear that you are in situation in which you have been targeted from all the sides of the life.
2. First, please work to convince your wife that they are not yours, because in this situation only wife can be a tough support for you.
3. Then you should not accept her plea that children are yours, let her prove this before the court of law, who knows you will come out of the unwanted demands.
4. And yes, for other criminal case on you, you should try to for the mediation won’t he consent of the other party and try to resolve the issue rather than totally settling it outside of the court as outside court settlement sometimes come out as a back out before the judge.