1. Unfortunately, if she files for a contested divorce, you will have to defend it and if you lose, the Court will pass a decree of divorce in her favour.
2. I assume, currently, you all are living altogether with. If she takes the daughter along with her, you will have to file a petition for guardianship of your daughter to reclaim her custody. 
3. In case of minors, the will of the minor child is immaterial as far as her wellfare is concerned, however, the court may take into consideration the willingness of your daughter, if she is able to make intelligent decisions. The provisions of Guardianship and Wards Act will protect your right to have your daughter back, if your wife takes her away from you and your daughter may be returned to you, if she testifies before the Hon'ble Court that she wants to reside with you, subject to, you have to show it to the Court that her welfare is better with you than your wife. 

In case wife files for divorce contest divorce proceedings 

2) file petition for RCR under section 9 of HMA 

3) your son is 19 years old and can decide whether he wants to stay with you of with your wife 

3) court would consider your daughter wishes before deciding custody issue 

4) you can file petition for joint custody of your daughter .seek interim visitation rights 

I would advise you to file a case for judicial separation, if you don't want the stigma of divorce on your collar and save the children from the stigma of their parents being divorced. Once you file that, you may file an application for restraining order against your wife in the same petition for her to stay away from your daughter and you.

Dear Sir/Madam,

No, you cannot be forced to give a mutual divorce; only the Family Court can grant divorce if your wife proves legal grounds under Section 13 of the Hindu Marriage Act.
Your 19+ son is a major, so no custody order applies to him. For your 14+ daughter, the court will see her welfare and can consider her own preference; your wife cannot simply take her away by force.
The relevant provisions are Section 26 of the Hindu Marriage Act and Section 17(3) of the Guardians and Wards Act.

1. If you do not want to give divorce you can challenge her grounds and refuse to accept her demand for divorce.

2. Divorce is between husband and wife only, the children cannot be separate from either of the parents due to the divorce proceedings.

3. If you forces your daughter, you can file a petition for custody and seek for no interference in taking care and upbringing of your daughter under the provisions of guardians and wards act.

You can start living separately with your daughter away from your wife and file a child custody against your wife on the grounds of what all you experienced and that had aggrieved you.

Since your daughter is above 14 years, the court will ask its opinion and take a decision accordingly in the interest of the child

If you are not ready for divorce she can file contested divorce against you. If you want custody of children you can file custody petition in family court. 

Firstly, you cannot be forced to give divorce merely because your wife wants it. Under the Hindu Marriage Act, 1955, divorce can happen either by mutual consent or by a contested petition. If you do not agree, she will have to file a contested divorce and prove legal grounds such as cruelty, desertion, etc. The court will decide based on evidence—your consent alone is not enough to grant divorce.

Secondly, regarding your children, custody is not automatically given to the mother. Courts decide custody based on the welfare of the child, which is the paramount consideration. Since your son is above 18, he is legally an adult and no custody issue arises for him.

As far as your daughter is concerned, the court will consider:
her age (14+),
her preference,
her welfare and safety, and
the conduct of both parents.

If your daughter is not comfortable with her mother and there are instances of physical abuse, this becomes a very important factor in your favour. Courts generally give significant weight to the child’s wishes at this age.

Your wife cannot forcibly take your daughter against her will. If she attempts to do so, you can immediately approach the court seeking custody or protection orders under the Guardians and Wards Act, 1890, and also seek restraining orders.

Further, physical abuse by your wife towards you and the children amounts to cruelty, which can also be a ground for you to take legal action. You may also consider filing:
a complaint for domestic violence, or
seeking custody orders proactively to protect your daughter.

In conclusion, you are not bound to consent to divorce, your children will not be automatically separated from you, and your daughter’s welfare and preference will be crucial. Given the allegations of abuse, it is advisable to document incidents and consider initiating appropriate legal proceedings to safeguard your and your children’s interests.

1) Can anyone force you to give divorce?
No, you cannot be forced to give divorce against your will. In India, divorce is granted only on specific grounds under Section 13 of the Hindu Marriage Act, 1955, such as cruelty or adultery. If your wife files a contested divorce petition, you have the right to defend it. The court cannot dissolve the marriage unless she proves her allegations. However, if she establishes "cruelty" (including your alleged refusal to talk or your children's behavior), the court may grant her divorce. But without mutual consent, no one can compel you to agree.

2) Will your children be separated from you?
Your 19+ year old son is a major and can choose his own residence. For your 14+ year old daughter, the court's paramount consideration is her "welfare". Since she refuses to talk to her mother due to past beatings, and you are the father (natural guardian under Section 6 of Hindu Minority and Guardianship Act, 1956), the court is unlikely to separate her from you unless you are found unfit. Your daughter's preference (given her age) will be considered. Physical violence by mother against child strengthens your custody claim.

3) Can she take your daughter against her will? Which section prohibits it?
No, she cannot forcibly take your 14+ year old daughter. Under Section 6(a) of the Hindu Minority and Guardianship Act, 1956, the father is the natural guardian of an unmarried minor girl. The Protection of Women from Domestic Violence Act, 2005 (Section 21) allows temporary custody to mother, but only if it is in child's welfare. Forcibly taking the child could constitute "kidnapping" under Indian Penal Code Section 361 (taking minor from lawful guardian without consent). The daughter's explicit refusal and her age (14+ years) will be given great weight by court.