Praise be to Allah.
We congratulate our sister on embracing Islam and we ask Allah to bless you with the guidance of your family and loved ones, and to help you to obey Him and seek His pleasure, and bless you with a righteous husband and righteous offspring.
Marriage in Islam is based on the proposal then the marriage contract. For the purposes of the proposal the man is allowed to see the woman and she is allowed to see him, so that the marriage will be based on clarity. That should be accompanied by asking about the man in order to find out about his character, religious commitment and condition, and the situation of his family. If he is good, then the basic principle is that he should be accepted, because the Prophet (blessings and peace of Allah be upon him) said: “If there comes to you one whose religious commitment and attitude pleases you, then marry [your female relative who is under your care] to him, for if you do not do that, there will be tribulation on earth and much corruption.”
Narrated by at-Tirmidhi (1084) from the hadeeth of Abu Hurayrah. Classed as hasan by al-Albaani in Saheeh at-Tirmidhi.
The fiancé is still a stranger to the woman, so it is not permissible for him to be alone with her, or to shake hands with her, or to look at her apart from looking in order to decide whether to go ahead with the proposal.
From this you will understand that Islam does not permit a relationship between a man and a woman who is not his mahram, even if that is for the purpose of marriage. This relationship is not permissible either before or after the proposal. But if there is a need to sit with the one who is proposing once or more in order to find out about his situation or to make arrangements for the marriage contract, there is nothing wrong with that so long as a mahram is present, and the woman wears proper hijab, and she treats him as as a man who is a non-mahram.
If your mother does not approve of the man for the reasons mentioned, which is that she thinks it is essential for there to be dating and a relationship and getting to know one another before proposing marriage, you do not have to obey her in her rejection of this man, because she is calling you to do something that is not permissible in Islam, and there is no obedience to any created being if it involves disobedience to the Creator. In that case you have to explain to her the ruling on these relationships and try to convince her of the marriage by telling her about some of the good qualities of the man after you have asked about him and found out about him.
If her rejection is for an acceptable reason, whether it has to do with religious or worldly matters, such as any shortcoming in his wealth or appearance, or something bad in his family and so on, then it is better to obey your moher.
If there is no acceptable reason for her refusal, then you do not have to obey her, but you should strive to please her and make her happy because of the great rights to kind treatment and respect that the mother has.
In order for the marriage contract to be valid it must done by the woman’s guardian, because the Prophet (blessings and peace of Allah be upon him) said: “There is no marriage except with a guardian.” Narrated by Abu Dawood, 2085; al-Tirmidhi, 1101; Ibn Maajah, 1881, from Abu Moosa al-Ash‘ari. Classed as saheeh by al-Albaani in Saheeh at-Tirmidhi.
The woman’s guardian is her father, then his father (i.e., paternal grandfather), then her son, then his son (i.e., grandson, if she has a son), then her brother through her father and mother, then her brother through her father only, then their sons, then her paternal uncles, then their sons, then the ruler. See: al-Mughni, 9/355
If the woman does not have any Muslim guardian from this list, the Muslim judge (qaadi) should do the marriage contract for her. If there is no Muslim judge, then a man of status among the Muslims, such as the Imam of the Islamic Centre, should do the marriage contract for her.
We ask Allah, may He be exalted, to help and guide you.
And Allah knows best.