What is the Shar'i ruling on the actions of the father and son regarding the contract for selling the gifted house, and is it permissible for the mother (to intervene), and is it obligatory for the son to return what he took from the house to be included in the inheritance?

The financial status of heirs is not considered in inheritances. The sale mentioned in the question is a sham sale, closer to a gift that requires proof of possession during the father's lifetime. If the sale was genuine, it must be proven with evidence, and the son is obliged to pay the price. These matters are complex and require referral to the Sharia courts. It is permissible for the mother to gift her two daughters from her share if the son is unjust and his injustice cannot be rectified. However, if the son is in the right, the mother must be fair among her children in giving gifts. If the son is a half-brother to the daughters from the father's side only and has another mother, then the mother is not blameworthy for specifically gifting her two daughters.