Welcome, we're glad you decided to post here.
I honestly don't think this has anything to do with her parents being good or not good Christians - it has everything to do with honor and respect in their culture. More than anything, it is a cultural issue that collides with their faith. They have to reconcile that but shoving in their face and that of your girlfriend is disrespectful. It isn't a matter of who's right and whose wrong here as followers of Jesus Christ. You can be right all you want, but it's not going to get you anywhere in this situation other than to cause division amongst everyone.
A meeting with their pastor would be helpful. He is a neutral party and can work at bringing you together. You need to hear out their objections with respect. As a family, if they want you to wait before moving forward in marriage, to get to know you better, then that is something to consider.
One of their objections is you are not Chinese, the other is - you come from a divorced family. That may not be valid to you, but it is important to them. In God's eyes you are all equal in color, but the divorce issue may be a huge one to them. This is where the pastor can say, I will spend the next 6-8 weeks with this couple and help them walk through any issues surrounding divorce in the family and your father's death and anything else they need to do to be a healthy couple ready for marriage.
Again, in their culture divorce may be absolutely disgraceful. For their daughter to marry someone who has divorced family members, is like putting a black seal on their family. Again, it's important to look at this from a cultural perspective.
Another thing to consider is, will this family continually influence your girlfriends decisions even once she is married? Will she be strong enough to stand up and set appropriate boundaries? This is where some pre-marital counseling would be helpful to you both. Otherwise, you could end up with a loyalty issues between you and a family that interferes too much.
Your girlfriend is obviously torn between her love for you and her love for her family. Making her choose is really unfair - she shouldn't have to at this point, you're not married.
Some things to consider -
1) If you run away together to get married - her family will probably disown her and that will cause great pain.
2) It is important to leave and cleave. This means leaving your parents and cleaving to your spouse once you are married. Sometimes parents have a really hard time letting go. This is something you need to seriously consider. Also, sometimes it is really hard when you have been close to your family, to also let go.
3) Honor and saving face are of huge importance in the Asian culture. You're right, her parents are probably worried about what other relatives are going to think. Is it important to them, obviously.
We've thought about writing them and the rest of her family all letters, because they can't immediately argue with written words.
I would recommend NOT doing this. The best way to talk through issues is face to face, not with letters. It will backfire on you. I'm speaking from personal experience on this one.
What are we doing wrong? Does God does not want this? Is he punishing us? Me?
Sometimes we want things very desperately, but God puts up warning signs and red flags in front of our face that say "whoa, slow down, take a deep breath, pray about this more, seek me more and
wait". The thing is, we don't to wait - we want to do it, when we want to do it and move ourselves ahead of god's work and plans for us.
Do you think he might be saying, slow down and wait? Have you prayerfully considered this? If there is still turmoil and uncertainty on your part or that of your girlfriend to move toward marriage, then that's a really good sign that you need to wait. If God is truly involved, there will be extreme peace about this decision, if not, then God's not part of the equation - your thoughts and desires are. And, that may not be what God wants for you - at least right now. It may mean WAIT.