Her father and brothers do not pray; can her younger brother act as her guardian in marriage?

Firstly: 

In order for the marriage to be valid, the woman’s wali (guardian) or the one who takes his place, such as his deputy, must be involved, because the Prophet (peace and blessings of Allaah be upon him) said: “There is no marriage except with a wali.” Narrated by Abu Dawood (2085), al-Tirmidhi (1101) and Ibn Majaah (1881) from the hadeeth of Abu Moosa al-Ash’ari; classed as saheeh by al-Albaani in Saheeh al-Tirmidhi. 

And he (peace and blessings of Allaah be upon him) said: “Any woman who gets married without the permission of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid. If they dispute, then the ruler is the guardian of the one who has no guardian.” Narrated by Ahmad (24417), Abu Dawood (2083), al-Tirmidhi (1102); classed as saheeh by al-Albaani in Saheeh al-Jaami’ no. 2709. 

Secondly: 

If the woman is a Muslim, then is essential that her wali should also be a Muslim, according to scholarly consensus. 

Ibn Qudaamah said: As for the kaafir, he cannot be the wali of a Muslim woman under any circumstances, according to the consensus of the scholars, including Maalik, al-Shaafa’i, Abu ‘Ubayd and ashaab al-ra’y. Ibn al-Mundhir said: All of the scholars from whom we acquired knowledge are unanimously agreed upon that. End quote from al-Mughni (9/377). 

Thirdly: 

If a person does not pray because he denies that it is obligatory, then he is a kaafir according to scholarly consensus. If he does not pray because he is lazy and heedless, then the scholars differed as to whether he is a kaafir or not, but the correct view as indicated by the texts of the Qur’aan and Sunnah and the views of the Sahaabah is that he is a kaafir. See the answer to question no. 5208. 

Based on this, the one who does not pray is not permitted to act as the wali or guardian in the marriage of a Muslim woman. 

Based on this, guardianship passes to the next closest relative (after the father), namely the grandfather. If there is no grandfather or if he is not fit to act as the wali, then it passes to her brothers. If the youngest of them is the one who prays , then guardianship passes to him if he is grown up, otherwise it passes to those who come after him, such as brothers’ sons, then paternal uncles, then their sons, then to the sharee’ah judge if there is one. See the answer to question no. 48992. 

In order to avoid hardship in this case, her brother or one who is fit to act as her wali – as discussed above – could do the marriage contract for you in the presence of two witnesses of good character, and this will be the valid marriage contract. As for the marriage contract done by her father, it will not be valid, but there is nothing wrong with you doing it with him, so as to avoid embarrassment and ward off problems, whilst striving to call him to pray regularly. 

We ask Allaah to help and guide you. 

And Allaah knows best.