How can deportation be removed?

Yes, you have to file to reopen your mother's court case and then once the court reopens and terminates your deportation then and only then you can apply for a Green Card.

It sounds as though you know what your next steps need to be. Given the time frame, you will need to have the government immigration attorneys agree to file a joint motion to reopen. You may also have some options under DACA you may want to explore.

By alerting immigration authorities about your presence in the U.S., you exposed yourself to a serious risk: an order of removal (deportation), once entered, remains valid indefinitely, until it is executed. Immigration and Customs Enforcement (ICE) has a duty to find and remove you; once you start filing applications with the Immigration Service, ICE's task becomes quite easy. Do not stake too much hope on your marriage to a U.S. citizen - it does not protect you from deportation automatically. Your spouse would have to prove to the Immigration Court that your removal would cause him/her an exceptional and extremely unusual hardship. While it is a difficult task in itself, you have an additional problem in that, unlike most of the people who are in the U.S. without permission, you don't have the right to have a hearing before an immigration judge. Even if you, somehow, manage to get your case to the Immigration Court, the court cannot hear the case unless the old deportation order is set aside. So, the situation is rather delicate and, even with a very skillful, professional handling, has rather high odds of ending badly. You need to find, as soon as possible, an experienced immigration law attorney who practices in the Immigration Court where your mother's case was decided 19 years ago: only that court, not the one where you live now, has the power to reopen the case.

You are correct that you will not be able to move forward in your case until the deportation before the Immigration Court is set aside. That can only happen in one of two ways. Either you file a motion to re-open directly with the Immigration Court and await their decision, or you can file a request with the ICE attorneys asking that they join in the motion to re-open before the court. You cannot do both at the same time, as the attorneys will not join if a motion to re-open is pending with the court. In my experience, it is best to work with the ICE attorneys, if possible, as the process is smoother.

If you have resided continuously in the US from June 15, 2007 to present, have graduated from high school or are currently enrolled in school, and have not been convicted of serious crime, you may qualify for deferred action for childhood arrivals (DACA) which would grant you a temporary work permit that you can renew every 2 years while the program is still valid. Otherwise, you will need to submit a motion with the immigration judge to reopen your or your mother's deportation case to allow you to apply for adjustment of status in court. On the other hand, if the judge agrees to both reopen and terminate your case, you can submit your I-485 application with USCIS instead.

You need to consult with a lawyer instead of this forum since a joint motion to re open to set aside the order of deportation based on available relief. This is very technical and a general answer is not a solution.