Live in relationships are dangerous to the extent if you have had a physical relationship and if she conceives during this period and thereafter if she alleges breach of promise to marry and alleges Rape on grounds of promise of marriage.
]But from what you describe your live-in relationship, it has not gone to that extent. However if you have texted her of your intentions of marriage during your 3 year relationship, she will likely to use these text messages as proof, along with other incidental proofs of your travel, such as photos, hotel bills, lodging receipts etc., to lodge a complaint against you.
If you cannot convince your parents about your intention to marry this girl why did you allow this relationship to progress for 3 years, you should have stopped it immediately.
If the girl is persistent in her demands for marriage and your parents are adamant they it is for you to choose between the two, you are an adult, if you were to take your parents side then you will have to face criminal charges that might be filed by this girlfriend of yours. If you love this girl choose her and avoid future complications.