All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, may Allaah increase your reward and have mercy upon your dead and relieve you from your calamity.
As regards the joint account, the money that is deposited in it is of two kinds:
1- If it belonged to your father, then it is part of the inheritance that should be divided amongst yourselves according to the Sharee’ah (the Islamic Law) and your mother has no right to take possession of it. She is only entitled to one-eighth of it. Also, she is not permitted to give from the inheritance in charity without the permission of the heirs. Moreover, she is not permitted to spend on herself from the inheritance.
2- If the money that is deposited in the account belongs to your mother, then it is her property and it is not included in the inheritance. If part of it belonged to your father, and another part belongs to your mother, then what belonged to your father is an inheritance, and what belongs to your mother is her own property and it is not included in the inheritance. The funeral expenses of your father should be taken from the inheritance of your father before dividing it on the heirs. Your grandmother (from your father’s side) has the right in the inheritance of her son; she is entitled to one-sixth. The fact that she is unconscious does not exempt her from her right; rather, she takes her share and it will be given to her guardian or any person whom the judge appoints to run her affairs. This person should dispose of her money according to what is reasonable, and if she dies before taking possession of her share, then it is transferred to her heirs.
Allaah Knows best.