It is apparent from your question that you yourself are not fully convinced that the woman you are in love with is really the one you want to marry. It is not only a question of this being an interfaith marriage, but also an intercultural marriage. You are Indonesian living in the United States. You don’t say where this woman is from, but I am assuming that she is not Indonesian, and thus from a different culture than yours.
One thing that concerns me is this: You say, “I have tried to show her my way of life; however it is difficult for her to accept. It is very difficult, but not impossible, to change a person who has been accustomed to a way of life of another faith.”
If I understand your words correctly, you want to change her to accept your faith and way of life—or at least you want her to accommodate herself to your lifestyle. No marriage can be successful if you go into it expecting the other partner to change to your expectations. What about you changing to accept her way of life (but not her faith)? What accommodations are you willing to make?
I feel that you are not as ready for this marriage as you might think you are. I advise you to ask our Ask the Counselor about this issue. I’m not a psychologist or counselor and can only give you my “gut feeling” rather than an expert advice.
As for your four questions, I can only answer some of them. (1) The children of a mixed marriage are to be raised as Muslims. Your responsibility as the father is to see that they are raised as Muslims, that they learn Islamic hygiene and manners and etiquette of eating, entering the bathroom, etc. Also that they learn to read Quran and how to pray.
It will also be your responsibility to see that they actually do pray. If your wife remains a Christian, this responsibility will be a heavy one on you. Are you willing to undertake it? And how much is she willing to assist? These are things that must be discussed before marriage.
(2) As for her rights to custody and inheritance or bequeathal, you must ask our Ask the Scholar Section. One thing you must understand (and should make clear to them in your question) is that if you continue to live in the United States (or any other non-Muslim country), the laws of that land are going to prevail over Shari`ah.
So if your children are born in the States and are thus US citizens, and your family is in Indonesia, if you die, the children will remain with their mother. No judge will send them back to your Muslim family, even if Shari`ah says they should go.
This is also something that you should discuss with her before you consider marriage. You should also discuss the possibility of your moving back to Indonesia with her and the children. You might not want to do it now, but you could change your mind later. Is she going to be willing to do that, and does she understand all the consequences of that decision if something should happen to you there?
(3) One of the things that makes me question whether you are really ready for this mixed marriage is your question of where to have the marriage ceremony. If you two cannot even come up with a compromise solution on such a simple issue, I don’t think you are ready for this marriage. To be valid, a Muslim marriage needs only two male Muslim witnesses, so it does not have to take place in a mosque. I believe a Christian marriage also only requires two Christian witnesses. So you can have the ceremony at the offices of the justice of the peace or in a public park or in a restaurant with a reception following.
(4) You ask, “What does Islam teach that can convince myself, my parents, and my peers that interfaith marriage is permissible and can be successful?” Once again, if you need convincing, then you’re not ready for this marriage. It is clear that interfaith marriage is permissible when it is a Muslim man marrying a Christian or Jewish woman (but not the opposite, i.e., for a Muslim woman to marry a non-Muslim man).
What makes it successful? The same as any other marriage: loving, caring, communicating, mutual respect. But in a mixed marriage it is even more important that you both discuss issues relating to religion and child rearing before marriage. And you should both enter the marriage with respect for the other’s beliefs but with no intention to change the other person, and no expectation that the other will change.
Also remember that you are considering not only an interfaith marriage, but an intercultural one. Another thing to consider is the role of grandparents, aunts and uncles. If your family is in Indonesia and her family in the States, your children will likely be influenced by her family (unless they live far away).
The children have a right to know and interact with their maternal relatives, but this can cause problems if her family insists on teaching Christianity to the children. All of these issues, and others, must be considered before deciding on this marriage. Please read the links provided at the bottom of this answer for more information.
Please make your decision after praying lots ofIstikharah Prayer (prayer asking God to help you make the right choice).