Praise be to Allah.
What counts in order for a marriage to be valid is the consent of the woman’s wali (guardian), which is her father in this case. As for the mother, it is not essential that she give her permission or consent, but it is recommended for the father to consult her as a sign of respect towards her.
Based on this, if the father of the girl agrees, then he can arrange the marriage contract with you, but is it right to go ahead with this marriage? That depends. If the girl is religiously committed and of good character, and the mother’s refusal is based on minor reasons or something that can be rectified in the future, then there is nothing wrong with going ahead with this marriage. But if her refusal is based on something that cannot be rectified soon, then it is better not to go ahead with this marriage, because the mother’s attitude may affect your married life.
Determining what is best in this case needs an examination of the details of the matter. But in general terms we may say that it needs you to weigh up the pros and cons, and to look at the nature of the girl and how much she is influenced by her mother’s attitude, if she will put pressure on her or tell her to go against you. As for your saying that you are still keeping her picture, if what you mean is that you have a photo of her, this is not permissible for two reasons:
1 – She is a stranger (non-mahram) to you, so it is not permissible for you to look at her. This looking is one of the doors that lead to fitnah. Hence Islam enjoins lowering the gaze, as it says in the verse (interpretation of the meaning):
“Tell the believing men to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts). That is purer for them. Verily, Allaah is All‑Aware of what they do”
2 – It is not permissible to keep photos for memories, even if they are pictures of one's sons and daughters or mahrams, because of the general meaning of the evidence which indicates that making images is haraam, and the stern tone of that evidence. It is not permissible to take pictures of animate beings except in cases of necessity and urgent need, such as ID photos and pictures of criminals and so on.
Based on this, you have to get rid of this picture and understand that Allaah is watching you and can see you, so fear Allaah and fear His punishment, and conceal the ‘awrah of believing women, and wish for them what you would wish for your own family of concealment and well being.
Do not marry until you ask Allaah for guidance (istikhaarah). Please see question no. 11981 for more information on Salaat al-Istikhaarah.
We ask Allaah to guide you.
And Allaah knows best.