Firstly: 

Allah has ordained divorce (talaaq) to dissolve the marriage contract, which is a firm and strong covenant. Allah says (interpretation of the meaning): “and they have taken from you a firm and strong covenant” [an-Nisa’ 4:21]. 

No one has the right to use divorce except in a serious manner and for a reason. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: The Lawgiver forbids treating the verses (laws) of Allah as a jest or to speak of the verses of Allah that are covenants, except in a serious manner that shows commitment to the shar‘i conditions and obligations. Hence it is forbidden to take them as a jest as it is also forbidden to engage in a tahleel marriage (in which an irrevocably divorced woman marries another man with the intention of getting divorced so that she can go back to her first husband). This is indicated by the words of Allah (interpretation of the meaning): “And treat not the Verses (Laws) of Allah as a jest” [al-Baqarah 2:231]. And the Prophet (blessings and peace of Allah be upon) said: “What is wrong with people who play with the limits of Allaah and take His verses (laws) as a jest, and one of them says, ‘I divorce you, I take you back, I divorce you, I take you back’?” Thus it is established that tampering with them (the laws and limits set by Allah) is haraam.

End quote from al-Fataawa al-Kubra, 6/65 

The hadeeth was narrated by Ibn Maajah, 2017; classed as hasan by al-Busayri in az-Zawaa’id; classed as da‘eef by al-Albaani in Da‘eef Sunan Ibn Maajah. 

Based on that, your father does not have the right to pretend to divorce when he does not really want to divorce in a real sense. 

Moreover, this pretence is a trick to consume wealth unlawfully. The state only gives this assistance to women who are really divorced, and using a trick to obtain it is haraam. 

Secondly: 

If divorce (talaaq) takes place with a clear statement using the word talaaq or its derivatives, then the divorce counts as such even if he did not intend it to do so. 

If it is written and not spoken, the basic principle is that it does not count unless it was intended as such. But if that occurred in court, then some of the scholars say that it does count as such even if the intention was not there. 

See the answer to questions no. 72291, 125215 and 126378 

If your father is unable to spend on his wife’s maintenance and he thinks that divorcing her in a real sense will enable the wife and her children to get this assistance, then he may do that. But he should bear in mind the implications of doing that, such as cancelling out the right to inherit from one another and other rulings. Our advice is to look for another means of earning a livelihood and spending on his family; that is better for him than divorce. May Allah grant him relief and a way out from this problem. 

And Allah knows best.