Praise be to Allah.

Firstly: 

The marriage contract is not valid except with a guardian; a woman does not have the right to give herself or anyone else in marriage, or to appoint anyone except her guardian to give her in marriage. If she does that, then the marriage is not valid. 

Please see the answer to question no. 99696 

Secondly: 

There are degrees of closeness for guardians according to the fuqaha’, and it is not permissible to overlook the more closely-related guardian except in cases where he is not present or he does not meet the conditions. 

The woman’s guardian is her father, then her paternal grandfather, no matter how far the line of ascent reaches, then her son, then his son, no matter how far the line of descent reaches, then her full brother, then her brother through her father, then the sons of said brothers, then her paternal uncle who is a full brother of her father, then her paternal uncle who is her father’s brother through his father, then the sons of said paternal uncles, then the next closest, then the next closest in kinship on the father’s side, as is also applicable in cases of inheritance. The Muslim ruler (or one who acts in his stead, such as a qaadi or judge) is the guardian of the one who has no guardian. 

Please see the answers to questions no 2127 and 136715

Thirdly: 

The guardian is obliged to give his female relative under his care in marriage to a compatible suitor whom she is pleased with, otherwise he is preventing her from getting married. 

Preventing a woman from getting married is haraam, because Allah, may He be exalted, says (interpretation of the meaning):

“And when you have divorced women and they have fulfilled the term of their prescribed period, do not prevent them from marrying their (former) husbands, if they mutually agree on reasonable basis. This (instruction) is an admonition for him among you who believes in Allah and the Last Day. That is more virtuous and purer for you. Allah knows and you know not”

[al-Baqarah 2:232]. 

Based on that, it is not permissible for a woman’s guardian to prevent her from marrying a compatible suitor, if she is pleased with him. But if she wants to get married to someone who is not compatible, then he has the right to prevent her from doing so and he is not regarded as preventing her marriage (in the prohibited sense). 

If he prevents her from marrying a compatible suitor with whom she is pleased, and there is no acceptable reason for preventing the marriage which based on her interests, then guardianship for her marriage passes from him to the next closest guardian, according to the order mentioned above. 

Shaykh Muhammad ibn Ibraaheem (may Allah have mercy on him) said: 

If a woman reaches puberty and receives a marriage proposal from someone with whom she is pleased in terms of religious commitment, character and compatibility, and the guardian does not see in him anything that would make him incompatible for a woman of her standing and cannot come up with a justifiable reason for not allowing this marriage, then the woman’s guardian is obliged to respond to his request to marry her. If he refuses to do that, then his guardianship is rendered invalid, and it passes to the next closest male relative on the father’s side.

End quote from Fataawa wa Rasaa’il Muhammad ibn Ibraaheem (10/74) 

See also the answer to question no. 36209 

Hence it is clear that what this suitor is saying, that it is essential to get your father’s agreement, is correct and sound, unlike the view of your mother who thinks that the engagement (and marriage contract) may take place without his knowledge. Moreover, what is customary among most people, even those who do not know the Islamic ruling requiring a guardian in the case of marriage, is the same thing; no man would propose marriage unless he can get the agreement of another man (i.e., the guardian) to the marriage. 

So try to explain the Islamic rulings concerning this matter to your mother, and ask some sincere people among your relatives and family members to intervene, so as to involve your father in an appropriate manner. 

If your father does not want to attend, then ask him to delegate one of your brothers, or one of his relatives or your relatives, to do the marriage contract instead of him. Then the marriage contract will be valid, as this proxy will take the place of the father and he will not have to attend. 

If he refuses, then as we have explained to you, the ruling is that guardianship passes from him to the closest-related guardian after him, according to the order explained above. 

We ask Allah to help and guide you. 

And Allah knows best.