Praise be to Allah.
You should not hesitate to give up this girl and keep away from her. The Shaytaan has clearly confused you both; he has made you do something haraam, and has made it appear attractive to you by making you think that it is obedience and drawing closer to Allaah.
What you say in your question is indicative of what we are saying. You say, “[Allaah] has guided me”, “she is advising me”, “she obeys me in anything that is pleasing to Allaah”, “we are cooperating in righteousness and piety” and “she reminds me of Allah”. All of these are words that are acceptable in Islam, but the Shaytaan has made them into lovers’ words.
We are certain that you would not agree for any of your own sisters or daughters to enter into such a relationship, would you? So why do you think that it is acceptable for other people’s daughters?
Do you think that if your own daughter did something like this, corresponding and speaking to a non-mahram man when she is engaged to one of your relatives, that you would approve of her actions, even if she were to say to you, “Allaah has guided this young man at my hands, and I remind him about Allaah, and we are cooperating in righteousness and piety, and I am advising him”?!
I do not think that you would like it if your fiancée were to correspond with a young man, or if a young man were to correspond with her on the grounds of “sincere advice” or “cooperating in righteousness and piety” etc.
No, by Allaah, we do not think that any wise person would accept this, so do not be deceived by the Shaytaan’s making your deeds appear attractive to you. End this relationship immediately and let this girl go; do not worry about what she may say to her husband, because you are not responsible for her and you have nothing to do with her. You don’t know – perhaps she will marry someone who is better for her than you!
You say that she is engaged, and the Prophet (peace and blessings of Allaah be upon him) said: “No man should propose to a woman to whom his brother has already proposed marriage.” (Agreed upon). So it is not permissible to do things the right way and approach her family, asking to marry her; so how can it be permissible for you to speak to her and correspond with her without her family knowing?
Fear Allaah, and leave her without any hesitation. Do not get in touch with her again. Leave her and her business and her family alone. Any woman who agrees to speak to non-mahram men when she is engaged or married cannot be entrusted with a household or with the upbringing of her daughters and sons. Beware lest Allaah punish you with regard to your own family and children. I ask Allaah to guide you and help you. Give this up for the sake of Allaah and Allaah will compensate you with something better than that which you have given up.
We ask Allaah to help you to do that which is best for you in this world and in the Hereafter.
And Allaah is the Source of strength.