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.
If your father has given the house as a gift to your mother and it was not done during a fatal illness that was likely to end in death and your mother took it into her possession, having full ownership over it, then this is considered a valid gift and the legal ownership of the house has been transferred to the mother. In this case, this house should not be included in the father’s estate to be distributed among his eligible heirs because it is no longer his property.
Your mother is not obliged to divide the house among her children during her lifetime; however, if she willfully chose to divide it among her children during her lifetime, then she should establish justice among them in this regard. The Prophet said, "Fear Allaah and observe equality among your children." [Al-Bukhari and Muslim] Parents are obliged to treat their children equally in terms of offering gifts if the rest of the children do not give their consent to other than it. This is the opinion adopted in Islamweb and it is the opinion of the Hanbalis. Other scholars, on the other hand, held that observing equality among children in terms of offering gifts is only recommended.
The following question arises: does equality among children mean giving the male the same share as the female or giving the male double the share of the female as is the case in inheritance? Scholars held different opinions in this regard. For more benefit, please refer to fataawa 128693 and 168531.
As for you buying the house at the price that you mentioned, it is considered buying a property at a price lesser than its due price so as to benefit the buyer. Muslim jurists held that when a person (owner) sells a property for less than its market price, the price difference is considered a gift offered to the buyer. If your mother sells you the house for that price, then the difference between the actual price and the one paid by you is considered a gift from your mother. It should be noted that offering you that gift without offering the rest of her children the same contradicts the due equality required of the parents.
As for the fact that you were helping your father financially, this is commendable dutifulness towards your father for which Allaah shall reward you. If you had helped him and offered him that money as a debt on him to you, then you are entitled to the same amount that you gave him, and this sum should be deducted from the estate of your father and not from the house, which is the property of your mother.
Your dutifulness towards your father does not justify that you take your mother’s house alone apart from your siblings.
Allaah Knows best.