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.
Also, he is obliged to sufficiently provide for the needs of his children. Ibn Al-Munthir said: “All of the noteworthy scholars that we know of have agreed that a man is obliged to provide the needs of his children who have no money, because the child is a part of him, and he (the father) is a part of his father. So just as someone is obliged to provide for his own needs and the needs of his wife, so is he obliged to provide for what is part of him (i.e. his children) and his origin (his parents).” [End of quote] Ibn Qudaamah quoted him as saying this in Al-Mughni.
Therefore, it is clear that one should provide for his child just as he provides for the child's mother. For more benefit, please refer to Fatwa 88825.
Secondly, in the Sharee’ah, it is permitted for a husband to lie to his wife and vice versa if it means achieving a correct objective, like maintaining good marital relations and marital stability, provided that this does not lead to any injustices. For more benefit, please refer to Fataawa 83133 and 96115.
Thirdly, it is permissible for you to gift the house to your son if you are in your good health and do not intend to exclude the other heirs. If you gift it to him and he gains possession of it, then it becomes his property even without documentation. However, documentation is better in order to avoid future disputes. For more benefit, please refer to Fatwa 127822 and 131650.
Allaah Knows best.