All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
A rational man does not need a guardian in order to marry; rather, he can marry by himself, or entrust someone to represent him in the marriage contract.
The guardian is only required to marry off a woman.
‘Aa’ishah narrated that the Prophet said: “Any woman who gets married without the consent of her guardian, her marriage is invalid, her marriage is invalid, her marriage is invalid.” [Abu Daawood, at-Tirmithi and Ibn Maajah]
For more benefit on the conditions for the validity of marriage, please refer to Fataawa 83629 and 86384.
The age difference is neither a religious nor a customary impediment for marrying a woman. Indeed, the Prophet married Khadeejah who was much older than him. If a woman has already been married before, then this is also not an impediment to marry her.
It is confirmed in the Sunnah that those who love each other are encouraged to marry as in the Hadeeth narrated by Ibn Abbas that the Prophet said: "The best solution for those who love each other is to marry.” [Ibn Maajah]
Therefore, it is acceptable to try to persuade your parents to agree to your marriage with this woman and you can seek the intercession of some rational people to convince them. If they are convinced, praise be to Allah; otherwise leave her and look for another woman because the scholars stated that the obedience of parents comes in priority over the desire of the son in marrying a specific woman, but they made an exception if it is feared that the son will commit illegal sexual intercourse with her; in which case, what helps him to keep his chastity and avoid what is forbidden comes in priority over the obedience of the parents.
The obligation of Allah is more emphatic to be fulfilled and obeying Him is more obligatory.
Nonetheless, if you do not marry this woman out of obedience to your parents, then this may be a reason to be enabled to marry a pious and righteous woman with whom you will be happy and you will be blessed with righteous offspring from her that will be a comfort to the eyes of both of you, Allah willing.
Finally, we warn you against forbidden affectionate relationships between a man and a non-Mahram woman; because that is a door to temptation and corruption.
For more benefit, please refer to Fataawa 84544, 186355, 83379, 92731, 153881, 101495, 106420, 134498, and 116872.
Allah knows best.