Praise be to Allah.
Firstly: It is not necessary to write a will with regard to the division of a person’s estate during his lifetime, because one of the conditions of inheritance is that the death of the testator be established. Once his death has been established, his estate is divided as prescribed in sharee’ah among his living heirs. That is because the share of each heir is defined according to sharee’ah, as Allah says (interpretation of the meaning):
“There is a share for men and a share for women from what is left by parents and those nearest related, whether, the property be small or large — a legal share”
It is better not to divide the estate too early (i.e., before death) unless the testator fears some kind of corruption or dispute among the heirs, or that the shar’i ruling will not be applied to his estate because he lives in a country that follows man-made laws and not sharee’ah. In that case he can write that in his will.
Secondly: If we assume that your possessions will be divided only among the people mentioned in the question – two sons, a wife, a mother, a maternal grandmother, a sister and a father (you mentioned that your father is alive and that he left you, and did not do his duty of spending on you etc, but he will inherit from you and you from him) – then the division of the estate would be as follows:
The wife gets one-eighth, and the father and mother each get one-sixth. The two sons takes the rest of the estate, shared equally between them. It is not permissible for you to bequeath anything to any of these people in addition to his or her legal share, because the Prophet (peace and blessings of Allah be upon him) said: “Allah has given each person who is entitled his rightful share, so there is no bequest to an heir.” Narrated by al-Tirmidhi, 2046; classed as saheeh by al-Albaani.
With regard to the sister, she is prevented from inheriting by the presence of the two sons and the father, so she does not inherit. The maternal grandmother is prevented from inheriting by the presence of the mother.
It is permissible for you to bequeath part of the estate to them (the sister and grandmother), so long as it is no more than one-third of the total.
You mentioned in your question that your mother gave you part of the house as a gift but you do not mention whether she gave your sister any part of it. If she did not give her any part of it then she has failed to be just in giving to her children. It is not permissible for a person to give something to some of his children and not others, or to favour some of them over others in gift-giving. Rather it is obligatory to be fair in giving, because of the hadeeth of al-Nu’maan ibn Basheer who said that his father brought him to the Prophet (peace and blessings of Allah be upon him) when he gave him a gift, to ask the Prophet (peace and blessings of Allah be upon him) to bear witness to that. The Prophet (peace and blessings of Allah be upon him) said: “Have you given something similar to all your children?” He said: “No.” He said: “Take it back.” Then he said: “Fear Allah and treat your children equally.” Narrated by al-Bukhaari, 2398.
Treating children equally means giving a son the equivalent of the share of two daughters, because this is how Allah has divided the inheritance, and there is nothing fairer than the division allocated by Allah.
Based on this, you should either give your sister one-third of that which your mother gave you, or return the gift to your mother, unless your sister willingly foregoes her rights, in which case there is nothing wrong with it. And Allah knows best.