She is annoyed by the constant demands from her husband’s father for financial support even though he is able to work and earn a living

Firstly: 

Undoubtedly obedience to parents, so long as it does not involve disobedience towards Allah, is one of the greatest of righteous deeds and acts of worship. This is a well-known basic principle in Islam. 

The father has the right to take whatever he wants from his son’s wealth, but that is subject to conditions, one of which is that taking it should not cause harm to his son and that he should not take from him in order to give to someone else. 

Moreover, he should not take from his son’s wealth in order to waste it on extravagances or buy things that he does not need. This is more obviously forbidden; in fact it is not allowed even if it is one’s own wealth and earnings, so how about if it is his son’s earnings? See the answer to question no. 9594. 

Secondly: 

Spending on the father’s maintenance is only obligatory if the father is in difficulty and unable to earn a living from a suitable job. If he is not in difficulty or he is in difficulty but he is able to earn a living from a suitable job, then his son is not obliged to spend on him, according to the more correct of the two scholarly opinions. 

It says in Minah al-Jaleel, 4/416: Spending on the maintenance of parents who are in financial difficulty is obligatory, even if they have a servant and a house that they need but are no more than is necessary. It seems that this is the case even if the father is able to earn a living. This is the view of al-Baaji and those who agreed with him. However al-Lakhmi says that rather he should be compelled to work in his profession, and this is the correct view and is the view of the author of al-Jawaahir. This is what appears to be the correct view by analogy with the son, because in order for it to be obligatory for the father to spend on his son, it is stipulated that the son should be unable to earn a living doing work that is not demeaning to him.

End quote. See: Haashiyat ad-Dasooqi, 2/523 

It says in Kashshaaf al-Qinaa‘, 5/481-482: 

We may sum up the conditions of it being obligatory to spend on a relative in the following points: Firstly, that those on whom he is spending should be poor, with no wealth or income to make them independent of means so that they do not need someone else to spend on them. If those on whom he is spending are well off and have sufficient wealth or income, there is no obligation to spend on them, because the condition is not applicable in this case. But if their wealth or income is not sufficient for them, then he is obliged to top it up. Secondly, the one who is supposed to spend on them should have sufficient wealth to do so that is surplus to what he needs to spend on his own maintenance and that of his wife and family. Thirdly, the one who spends should be an heir of the one on whom he spends, either according to the shares allocated by sharee‘ah or because of blood ties through the father.

End quote.  

Thirdly: 

The husband does not have the right to take from his wife’s wealth in order to give it to his father, mother or siblings without her consent. It is not permissible for the husband to take anything of his wife’s wealth except what she gives willingly. 

See the answer to question no. 163541. 

What we think is that the son should give his father something by way of upholding ties of kinship, in such a way that will not adversely affect your needs and will not be unfair to you, and he and his siblings should encourage their father to work. 

You could make your salary separate from your husband’s salary, and save all of your salary, and your husband can spend on you and the children and shoulder the responsibility of living costs. This is his basic duty in the first place. Then if there is anything left over, he can use that to uphold ties with his father in a way that will not adversely affect you or be unfair to his children. Then he can add whatever is left over to what you have of wealth, and you can put that towards buying a house or you can save it for your needs. 

But you have to be very careful not to let that choice lead to trouble in your relationship with your husband. However, you are in a position to evaluate the situation as you are living with him. 

If you are afraid that that may lead to some trouble, then carry on as you have been doing, and try to advise him to think of what is best for you and your children whilst avoiding cutting off ties with his father or failing to uphold ties with him and treat him kindly, in ways that will benefit him and not harm you. 

See also the answer to question no. 130599.