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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If the situation is as mentioned, then the will of your father to his second wife is not valid as the Prophet said: "Allaah has given everybody his right, so there is no will for an heir." [An-Nasaa'ee, Al Tirmithi and Abu Daawood] If the father died while his wife was still under his guardianship, then she has no right in the will unless the heirs permit it. However, it is permissible to make a will for the step-children provided that it does not exceed a third of the inheritance because when Sa'd asked the Prophet whether he could make a will dividing all his wealth as charity, the Prophet replied: "No". He then asked him: "What about half of my wealth? The Prophet again said: "No." Then he asked: "What about a third of my wealth? The Prophet then said: "A third is acceptable, and it is a lot. It is better to leave your heirs rich rather than to leave them dependant on other people." [Al-Bukhari and Muslim] So it is permissible to make a will of a third of the inheritance for them because they are not among the heirs as it is permissible for a person to make a will before his death about a third or less of his wealth to other than the heirs as a way of giving in charity. The Prophet said: "Allaah permitted for you to give in charity a third of your wealth at the time of your death in order to increase your reward in the Hereafter." [Al-Bayhaqi] Imaam An-Nawawi said: 'The scholars agreed in a consensus at the present time that a person who has an heir cannot make a will to give in charity more than a third except with the approved of the heir.'
Therefore, the will of your father to his second wife and her children from the previous husband has to be looked at. His will to his second wife is not acceptable, but his will to her children is acceptable provided it does not exceed a third. So if the house equals a third of the inheritance or less than a third, it is acceptable, but if it exceeds a third then what exceeds the third is not acceptable. The remainder of the inheritance should be divided according to the Book of Allaah and the Sunnah of the Prophet .
This father should fear Allaah and not exceed His limits, as Allaah says after mentioning the verses regarding inheritance (which means): {These are the limits (set by) Allaah (or ordainments as regards laws of inheritance), and whosoever obeys Allaah and His Messenger (Muhammad ) will be admitted to Gardens under which rivers flow (in Paradise), to abide therein, and that will be the great success. And whosoever disobeys Allaah and His Messenger (Muhammad ), and transgresses His limits, He will cast him into the Fire, to abide therein; and he shall have a disgraceful torment.}[Quran 4: 13-14].
Finally, it is an obligation on the children to be kind and dutiful to their father as Allaah ordered them to do so even if he is negligent towards their right as Allaah is going to ask him and ask them about everything, so each one should fulfil the Commandment of Allaah.
Allaah Knows best.