Being adult, it mother  who can decide with whom to live. There is no legal solution. But if there is cruelty, harassment or violence against her, you can approach Court of Magistrate  under Protection of Women from Domestic Violence Act, 2005. Anyone is entitled to file a complaint  under the  Act if the  victim is unable or prevented from complaining. In the  complaint  you can also seek custody of mother .

You can file petition seeking custody of your  mother as she is suffering from dementia 

notice would be issued to father and brother 

court would peruse medical reports and then pass orders 

File an application in terms of section 14 of the RPWD Act 2016, and seek limited guardianship of your mother. Attach proof of mental illness of your mother. Make your father and your brother opposite parties in this matter.

better you seek a lawyers help. 

Mental health care act, 2017 focuses on mental healthcare and services, and the rights of persons with mental illness during healthcare delivery. 

While early-stage dementia patients may manage with some support, as the disease progresses, many require increasing levels of care, potentially including 24-hour supervision and assistance with daily tasks. 
Here's a more detailed explanation:

Dementia symptoms typically worsen over time, and the severity can range from mild to severe, eventually impacting a person's ability to perform basic daily activities. 

In later stages, many individuals with dementia require 24-hour care and supervision to ensure their safety and well-being. This may involve constant monitoring to prevent falls, wandering, or other potential hazards. 

Currently, there is no cure for dementia, but treatments can help manage symptoms and improve quality of life. 

you can narrate the incidents of her ill treatment by your father and deteriorating health condition due to the arrogant behavior of your father and take legal action as suggested by incorporating the above points in your application 

- You can issue a notice to your father against his said behavior with you and the mother , and further ask him to either to treat mother  with a doctor or to handover her custody to you. 

- You can also lodge a complaint on behalf of your mother to the police and higher official for his said negligence of mother and her health. 

- Further, if no positive response then file a petition before the Court. 

Dear client,

Since your mother is suffering from dementia and Alzheimer's and your father is not treating her appropriately, you have a legal option to seek her custody/guardianship. There are the following ways through which you can proceed.

1. File for the guardianship under the Maintenance and Welfare of Parents and Senior Citizens Act, 2007, to the district tribunal, citing the neglect and mistreatment by your father.

2. To strengthen your case, gather the medical reports proving her conditions.

Hope this helps you; if you still have any clarifications or issues, do not hesitate to ask.

You don’t need courts order to take care of your mother. You can initiate proceedings against your father for maintenance even if he doesn’t show income in ITR based on his property 

You can file a petition seeking leave for having custody of your old and ailing mother for her welfare since your father himself id old and have no adequate earning for treating your mother.

if there is any tribunal set up under the Right of Persons with Disabilities Act, 2016, then you will have to file an application before such tribunal seeking guardianship and custody of your mother

if there is no such tribunal then you will have to approach the High Court by filing a writ petition and invoke its 'parens patriae' jurisdiction for the above purpose

1) if you’re able to prove that father is unfit to act as a guardian for your mother, then only court would award you guardians, ship,

2) further if your mother Select your father, then your chances of success are bleak 

3) you need your mother‘s medical reports to prove that she is suffering from dementia.

4) medical prescription is not sufficient. You need mothers, diagnostic reports,

1. It is necessary that her mental health should be established first to claim her custody given that she is devout wife scared of husband and cannot remember for more than 30 minutes. Get her referred to district medical board of committee medical expert in relevant field to ascertain mental capacity. You can seek such certificate of disability from District Level Committee appointed under Section 72. Once her mental health is established, it is proved that she cannot take care of her, you can claim her custody.
2. If there is any violence you can also approach Session Court under Section 84.

most of your queries in your follow up are in the form of predictions

an advocate cannot predict what exactly will happen

what defence your father and brother will take to oppose your plea of guardianship cannot be predicted

everything in Court is unpredictable

if you knock on the doors of the Court you must be ready for any surprises. Then you cannot tell the advocate that - ohh you did not tell me this!

i dont think any tribunal has been set up under the RPwD Act 2016

so you will have to approach the High Court

your father and brother will be made respondents

what defence they come up with to oppose your petition, you want an advocate to predict for you?!

you will have to show that your mother is not in safe hands being with your father and brother. 

as regards the medical tests, the Court will direct an independent third party medical assessment of your mother

if she is not in a state to decide then considering the other attendant circumstances, the court may, upon being satisfied about your bonafides, grant guardianship to you even if your mother says that she is with her husband

all other acts mentioned in your follow do not apply in my view

and please be very careful when you decide to approach the High Court. If the Court finds that there is some mischief or oblique motive in filing the guardianship petition then the Court will not shy from imposing heavy costs on the Petitioner

No he can’t stop you as aforesaid 

First of all without taking any steps to get custody of your mother, how can you predict what steps your father will take to stop you from taking guardianship o custody of your mother.

You have to get a medical certificate from a competent medical examiner of the district certifying her illness and also to certify that she is not being taken care by her husband properly.

For this you can even approach social protection officer who will make a discreet enquiry and submit a report about the suffering she is being subjected to.

The medical prescriptions are not proper medical documents to establish your claim.

Your younger brother is also the son of your mother hence he too has a right to take care of her, in that case you have to prove that he too was involved in the acts of cruelty against your mother along with your mother.

Besides if your clearly stands by the side of her husband all your efforts will be in futile.

Especially if you are not able to take your mother outside then it will not be possible for you to obtain the requirements to file the desired custody case or guardianship case too.

1. You can apply for full guardianship under Guardianship under Mental Health Care Act, 2017. Courts prefer competent adult children as guardians over spouses in cases where the spouse is incapable of providing proper care and are negligent in taking care of the person not having the mental capacity to take their own decision.

2.  If your father has no means to support her (as per ITR), you can argue that you are better suited to be her guardian as per Maintenance and Welfare of Parents and Senior Citizens Act, 2007. You can also adduce documentary evidence to prove negligence/ ill-treatment to support your case.

1. The case is related to the welfare of your ailing mother for which you are seeking her custody.

2. For the said purpose, you shall have to prove that her welfare is in jeopardy being with your father since he, being an old person himself, is not capable of acting as a caregiver to your mother who is a patient of A.D.

3. You can file a Writ Petition seeking her custody for her welfare and the Court might ask for Doctors advice in this regard before deciding on the matter.

- The Court can take suggestion from a certified doctor for knowing her condition and her treatment & care by your father and said brother. 

- Otherwise , your consent is needed for getting guardianship .