Praise be to Allaah.
One of the blessings that Allah has bestowed upon you, your mother and your brother -- in fact it is the greatest blessing that Allah has bestowed upon all of you -- is that He has guided you to true faith and opened your hearts to the religion of Islam. We ask Allah to increase you in faith, certainty, guidance and piety, and to make you steadfast in doing that which He loves and is pleased with until you meet Him.
One of the Islamic duties that you must do, after Allah has guided you, is to strive to guide your grandmother by all possible means and tell her about that to which Allah has opened your hearts, whilst taking into account her age and what is usually the case with people of this age, namely attachment to the ways of one’s forefathers and the old, inherited religion. So use a gentle approach in seeking to guide her and try to be as gentle, kind and patient as you can, in the hope that Allah may guide her at your hands and open her heart to His religion.
If the bindi (red dot) that your grandmother asks you to wear is a sign of the woman’s religion and signifies that she is a Hindu or a follower of some other religion, then it is not permissible for her to wear it, because this comes under the heading of haraam imitation of the kuffaar.
If the bindi referred to is something that is common among women in India and there is no difference in that regard between Muslim women and others, then there is nothing wrong with wearing it from this point of view. But then we must think of it in terms of being an adornment first of all. If wearing this dot is an adornment in and of itself, that attracts attention to the one who wears it and makes people look at her, it is not permissible to wear it. But the issue of adornment is less serious than this issue of resembling or imitating the kuffaar, and your mother can conceal this red dot with her hijab or by covering her head and so on.
What matters is that you try to be gentle towards your grandmother as much as possible, without doing anything that is clearly contrary to sharee‘ah, until Allah makes things easier for you and grants you a way out, and enables you to be independent of your grandmother’s support. You should try to find suitable work, first and foremost your brother, then any of you who is able to find a suitable job that does not involve anything that is contrary to sharee‘ah.
And Allah knows best.