Do they have the right to declare their father legally incompetent and deny him access to his wealth, because he has grown old and senile, and he squanders the money?

The majority of scholars regard it as permissible to declare an adult man legally incompetent and deny him access to his wealth, if he is not of sound mind and cannot take proper care of his wealth, or if he will waste it, or he has lost his mind, or he is mentally ill. 

The one who does not handle wealth properly is regarded as foolish or feebleminded by the fuqaha’, because he wastes money and spends it inappropriately, in ways contrary to those indicated by Islamic teachings and common sense. 

Based on that, wastefulness that stems from foolishness is a valid cause for denying access to wealth, according to the majority of fuqaha’, the Maalikis, Shaafa‘is and Hanbalis. It is also the view of our two companions, Abu Yoosuf and Muhammad ibn al-Hanafiyyah, and is the basis of fatwas issued by them. 

End quote from al-Mawsoo‘ah al-Fiqhiyyah, 4/194 

It says also in al-Mawsoo‘ah al-Fiqhiyyah, 17/92: There is no difference of opinion among the fuqaha’ regarding declaring an insane person legally incompetent and denying him access to his wealth, whether his insanity is permanent or temproary, and whether it is strong or mild. 

Similar to one who is insane is the man who has grown old and senile to such an extent that he cannot handle his wealth or organize his affairs properly. 

Ibn Qudaamah said: Ahmad said: The elderly man who has lost his mind should be declared legally incompetent and be denied access to his wealth; his case is like that of one who is insane, because as a result of that he is unable to handle his wealth in a proper manner and protect it. Hence he is akin to the minor and feebleminded.

End quote from al-Mughni, 6/610 

Al-‘Imraani said: The evidence for it being allowed to declare the feebleminded, the minor and the insane legally incompetent and deny them access to their wealth is the verse in which Allah, may He be exalted, says (interpretation of the meaning): “But if the debtor is of poor understanding, or weak, or is unable himself to dictate, then let his guardian dictate in justice” [al-Baqarah 2:282]. “Of poor understanding” includes the one who squanders his money and the one who is denied access to his wealth because he is a minor.

“Weak” includes the elderly and senile, minors, and the insane. 

Allah, may He be exalted, tells us that their guardians should act on their behalf with regard to their rights and duties, which indicates that it is allowed to declare them legally incompetent and deny them access to their wealth.

End quote from al-Bayaan fi Madhhab al-Imam ash-Shaafa‘i, 6/207 

Ibn Abi Shaybah (may Allah have mercy on him) narrated in his Musannaf (6/291) that ‘Abd al-Malik ibn al-Mugheerah said: Najdah wrote to Ibn ‘Abbaas to ask him about the old man who has lost his mind or become senile. He wrote back to him, saying: If he has lost his mind or become senile, he is to be denied access to his wealth. 

Al-Mirdaawi said: al-Maroodhi said: I think that the son should declare his father legally incompetent and deny him access to his wealth if he spends extravagantly, or wastes it on immoral pursuits.

End quote from al-Insaaf, 5/333 

Based on that: 

If it becomes apparent that your father has lost his mind or the way he conducts his financial matters is objectionable, then there is nothing wrong with you referring the matter to the Islamic judge (qaadi) to examine his case and rule whether or not he is to be declared legally incompetent and denied access to his wealth, according to what the qaadi finds from his examination of the case and the comments of experienced specialists. 

That is because declaring a person legally incompetent and denying him access to his wealth is a judicial matter that can only be done on the basis of a ruling from the Islamic judge, as is the view of the majority of scholars. 

Ibn Qudaamah said: No one can declare a person legally incompetent and deny him access to his wealth except the judge (qaadi). This is the view of ash-Shaafa‘i… because spending extravagantly may vary and is a subjective matter, and each case must be decided on its own merits. Therefore, it cannot be decided except by the opinion of a qaadi. 

End quote from al-Mughni, 6/610

See also al-Mawsoo‘ah al-Fiqhiyyah al-Kuwaitiyyah, 17/96-97 

And Allah knows best.