Is it permissible for a divorced woman to marry a man in a secret, legitimate marriage, with witnesses, but without a guardian, due to her estrangement from her family or their refusal of her marriage? And is it valid for her son to be her guardian? And is the contract considered valid?

A woman may not marry without a wali (guardian). If one of her sons is an adult, he can be her wali. The marriage contract would be valid even in the presence of her father or grandfather, based on the madhhab (definition) (school of thought) of Imam Malik and those who agreed with him. It must also be emphasized that severing ties of kinship, especially with parents, is forbidden. It is obligatory to honor and be good to them, and to repent from abandoning them.