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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The solution lies in taking your case to an Islamic court that is able to solve such a dispute. Nonetheless, what we can say at the moment is that presenting a document stating that your mother is alive while in reality she is dead is a lie and it is forging documents and this is something which the law penalizes. Similarly, the gift that was given to your sister by the will is of no value Islamically, because a will for an heir is forbidden and it does not take effect unless all other heirs agree to it. Thus, it is better to take the case to an Islamic court, as Allaah The Almighty may deter by the ruler (i.e. by him enforcing penal laws) what He does not deter by the Quran.
As for the method of dividing the inheritance, then firstly, before dividing the inheritance on its rightful heirs, the debts of the deceased must be paid because the debt comes in priority over the right of the heirs in the inheritance. After paying the debts, the inheritance should be divided amongst them each according to his legal share.
If the deceased did not leave any heirs other than those mentioned in the question, then her husband gets one-fourth as his legal share due to the existence of direct heirs (children) as Allaah The Almighty Says (what means): {But if they have a child, for you is one fourth of what they leave, after any bequest they [may have] made or debt.}[Quran, 4:12] The remainder should be divided amongst the two sons and the three daughters by Ta’seeb (by virtue of having a paternal relation with the deceased and not having an allotted share, so they get what is left after the allotted shares have been distributed); the male twice the share of the female as Allaah The Almighty Says (what means): {Allaah instructs you concerning your children [i.e. their portions of inheritance]: for the male, what is equal to the share of two females.}[Quran 4:11]
However, the grandson [the son of the son] and other mentioned heirs do not get anything from the inheritance because they are prevented from it by the existence of direct sons. Therefore, the inheritance should be divided into 28 shares, the husband gets one-fourth, which is 7 shares, each son gets 6 shares and each daughter gets 3 shares.
Allaah Knows best.