It is good to hear that you're already trying to fix the problem by
physically staying away.
To have a relation, whether physical or verbal, with a na-Mahram is haram
and forbidden in Islam. It means to go against Allah (a)'s command and the
action will only deprive you if HIS Extra Mercy.
I would suggest you first let her study Islam regardless of your relation
with her. Let her explore and see if she can really accept Islam with her
heart and mind because accepting it without this holds no meaning to the
After she has accepted Islam, you can then approach the family for a
decent proposal and get your mutah recited to become Mahram with one
another and be free hence forth.
To get a better understanding on the last paragraph please refer to :