Is the husband obliged to spend on his wife’s mother?

The husband is not obliged to spend on his wife’s mother; rather he is obliged to spend on his wife and his household members on a reasonable basis.

But he should be generous to his wife’s family, and help them if they are in need, even if that comes under the heading of his charitable giving or zakah.

This is emphasised even more in this case, if his wife’s mother has no one to spend on her, as mentioned in the question.

If the wife knows that her husband would willingly give some things, such as food and similar things that people are usually easy-going about, there is nothing wrong with her giving such things to her mother, in a way that will not affect her own household costs, even if she does not clearly ask her husband for permission, so long as she thinks it most likely that he will overlook such things and will not prevent her from doing it. In that case, she will have reward and so will he.

It was narrated that ‘Aa’ishah (may Allah be pleased with her) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “If a woman gives food [in charity] from her house, without causing any harm, she will have her own reward for what she gives, and her husband will have his own reward for what he earned, and the storekeeper will have a similar reward, without any of them detracting from the reward of the others in the slightest.” Agreed upon.

And Allah knows best.