Is it permissible for a woman who wishes to commit and wear the niqab to uncover her face, even though her husband does not help her in this regard?

If the obligation of the hijab (definition) is your preferred view, or if you have committed to it by following those who consider it obligatory, then it is not permissible for you to remove it. You are not obliged to obey your husband if he orders you to remove it, because "there is no obedience to a creature in disobedience to Allah Almighty."

And assuming it is not obligatory, wearing it when speaking to a non-mahram (definition) man is better and more modest, with the caveat that it is not permissible for a woman to speak to a non-mahram man except out of necessity and while observing the Sharia (definition) guidelines, such as not speaking in a soft tone. The husband should help his wife in matters of goodness and righteousness.