How do I obtain forgiveness from an angry Mexican mother?

I have apparently offended the mother/family of the man I love and it is keeping us from having any sort of relationship. I have been told that it is a cultural dilemma. They are a Mexican-American family and are holding a grudge against me. This issue has lasted for months, and just gotten worse as time has passed. I love this family with all my heart! They are the coolest people I have ever met! How do I mend my relations with them as individuals, as well as my relations with them as a family unit?