Dear Sir, 

Considering the fact that you are residing separately it is better that you go in for a divorce. If possible a mutual consent one if your wife is ready. Further your children are old enough to understand the situation and joint custody of the younger one can be sought for as the child is still a minor. You can continue to maintain them financially. 
As for your wife I doubt she will step in for a mutual consent to she already is making allegations against you but still there is no harm in trying considering that you can provide for maintenance and alimony 

File for divorce on grounds of mental cruelty 

2) wife abusing husband amounts to mental cruelty 

3) wife refusing to have sex amounts to mental cruelty 

4) seek joint custody of children 

She has been constantly troubling and torturing you for one or the other reasons including threats of filing false cases and refusal to cohabit.

All these constitute acts of mental cruelty.

Therefore you can decide about filing a contested divorce case on the grounds of cruelty irrespective of the repercussions because it clearly appears that you may not be able to continue with the marital life in the given situation.

You cannot ask for custody of the adult child who is aged 20 years but of course you can think about seeking  for custody of the younger child which would become an adult within two years.

You look for the relief whichever is feasible now. 

One child is already major and other is nearby. No question of custody arise. They  are free to decide their own course. 

Dear Client,

Given your situation, you can consider filing for divorce on grounds of cruelty, which includes mental and emotional abuse, and the consistent threats and false accusations by your wife. Document all instances of her abusive behavior and threats, as well as any efforts you made to reconcile or seek counseling. This evidence will support your case in court. Since marital rape is a serious accusation, be prepared to provide evidence or witnesses that can refute her claims.

Regarding joint custody of your children, you can file a petition for joint custody during the divorce proceedings. Courts generally consider the best interests of the children when determining custody arrangements. Highlight your active role in their upbringing and your capability to provide for their welfare despite your financial difficulties. The court will evaluate both parents' ability to provide a stable and nurturing environment. Consult with a family law attorney to guide you through the legal process and to ensure your rights and interests are protected.

1. There are a slew of matrimonial remedies available to you like judicial separation, restitution of conjugal rights, divorce etc.  Which remedy best suits your purpose can be adviced to you, only on exhaustive consultation session. You need to visit me for that. 
2. I'm based in Mumbai /navimumbai just as you are.  So it shouldn't be much of an issue for you to visit me 
3. ९८२०८९७८८४ (nine eight two zero eight nine seven eight eight four) 

- As per law, if wife is not supporting her husband for the enjoyment of life and denying relation, then the husband can get divorce after filing a divorce petition before the court on this ground.

- Further, As per Delhi High Court, physical intimacy is an essential aspect of marriage and a wife's continuous refusal to have such relationship with her husband can be a ground for divorce,

- If she is not interested to live with you , then you can take her consent for mutual divorce with the condition of joint custody and only a minimal alimony amount. 

- Further, if she denied then you can file a divorce petition before the court on the ground of cruelty , however she can claim maintenance from you  

- As per Madhya Pradesh & Allahabad High Court , Unnatural Sex By A Man With Wife Not Rape.