All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we advise you to be patient with your wife especially that you mentioned that she does everything correctly. So, you should try to convince her in a wise manner and with good words about Hijab, but you should not hasten to do anything that you will regret later, let alone to divorce her.
As regards separating from her, if you mean that she will stay as your wife while you spend on her but you stay away from her and you keep her hanging neither married nor divorced, then this is not permissible except with her permission. Therefore, you are religiously required either to keep her in kindness or divorce her in kindness.
For more benefit, please refer to Fataawa 86618 and 88304.
On the other hand, you should know that the parents have a great status and that Allaah ordered us to keep good company with them even if they are non-Muslims and they dispute with us and try to turn us back from our religion, as Allaah Says (what means): {But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in [this] world with appropriate kindness}[Quran 31:15] Therefore, if your parents are Muslims, then you should keep good company with them and be patient with them with greater reason.
As regards separating from them, if this separation does not lead to cutting the relationship with them or undermining the minimum dutifulness and kindness to them, and there is a need for doing so or a preponderant benefit while keeping ties with them and they are not harmed by this, then this is permissible. However, if this leads to cutting the ties with them, or that they are harmed by this, then it is not permissible to do so. In any case, it is better to be patient with them.
For more benefit on being kind and dutiful to the parents, please refer to Fataawa 82254 and 84942.