Is it permissible to marry secretly without the parents' knowledge due to their refusal, while fearing the mother's wrath?

First, you must stop communicating with this foreign woman to avoid temptation (fitnah). If both of you are attached to each other and you are able to marry her, then that is good, for the Prophet, peace and blessings be upon him, said: "Nothing is seen for two who love one another like marriage."

Strive to convince your mother with the help of good people and through supplication (du'a). If she insists on refusing, and her prevention is out of stubbornness or you fear falling into what is forbidden (haram), then you are not obliged to obey her.

If it is facilitated for you to marry her, then work on teaching her her religion and raising her, and be a good role model for her. If you prefer to be dutiful to your mother and forgo marrying her, seeking another righteous woman, Allah may facilitate for you a righteous woman through this dutifulness.