I am assuming that you are a sister. The short answer is no, your parents don't have to be present if they are not willing, assuming that they are not muslim.
If your father is not Muslim, and neither is any male member of your family, then your representative in the Nikah ceremony will have to be appointed for you, unless you choose one yourself.
So a nikah contract consists of 2 things: kubool
. Before anything starts, you as the bride-to-be have to give your consent to the marriage to your representative, either verbally or by a written note. After you consent, the kobool and ijaab can take place.
- The kobool
part entails that the representative of the bride says to the groom : "I hereby give you my daughter/sister in marriage according to the Quraan and the sunnah of the prophet
- The ijaab
part entails that the husband says to the representative of the bride: " I hereby accept your daughter/sister as my wife".
An imam has to officiate the proceeding and 2 male witnesses of good reputation have to be present and sign that they witnessed the marriage. Then you, your nikah represantative, the husband and imam sign the contract.
Usually, in N. America anyways, a civil marriage license HAS to be issued before the nikah can take place. This ensures that the marriage is performed according to state/province regulations. If only a religious marriage is performed (i.e., only nikah contract without state issued marriage license) the marriage will NOT be recognized by the state.
Any conditions to the marriage must be stated in the contract at this time. Issues like bride gift (mahr/sidaaq) will have to be specified in the contract. Other things can be specified as well. Obviously these things/conditions should be discussed well before the nikah ceremony - they should be agreed upon by the two sides by the time of the nikah.
Having said that, it would be nice to have your parents attend the marriage even if they are not muslim. They are your parents and attending a daughter's marriage is a once in a life time event. I am sure they can be persuaded to come. Whether they are Muslim or not does not negate that they are your parents who raised you and took care of you. Try to reason with them and let them know that you really want them there.
The marriage/nikah does not have to be performed in a masjid, it can be performed elsewhere (e.g. a restaurant, a banquet hall) if the masjid is a thorny issue for your parents. Try to find a way to include them.
That's my opinion anyways, I hope you found this useful....
and mabrook in advance