Well, first we need to make sure that you do not spend more than 180 days outside of the U.S. and that you do not have multiple trips outside of the U.S. that add up to 180 days within any 12 month period. This is to make sure that you do not lose your Residency through abandonment. Then we have to work on removing the conditions of your Residency. You would start the divorce process in PA. Since you have not stopped residing there for more than 6 months, you are still considered under their jurisdiction and obviously so is your spouse and daughter. So PA is where you need to file. Once you start the divorce process, you will need to file an I-751 in waiver form. Here is a link:
Then you would collect evidence to prove the relationship was real but just fell apart. It can include any and all of the following:
A letter where you describe, in a very detailed fashion, the circumstances in which you met your spouse, the reasons you married, and the feelings and emotions that you had or still have towards your spouse, and why.
If you have a child or children together, the birth certificate for each child.
Wedding pictures and pictures of other moments when you and your spouse, and other members of your families and friends have been together.
Very detailed letters from people who know you and your spouse and who are witnesses that your marriage was valid, who were at your wedding, or who knew you as a married couple.
Love letters or cards that you received from your spouse while in the relationship.
Letters from people addressed to both you and your spouse, or in which the person who wrote the letter refers to both of you as a couple.
Any types of documents that have both your names on them that show that you bought a car, a house, furniture, or anything else together.
Any rental or lease agreements for your home or apartment with both of your names on it or a letter from the building manager or owner proving that you lived together.
Bank or financial statements that show that you had or have a savings or checking account together.
Any insurance documents that show that you were or still are covered by your spouse's insurance plan, or that your plan covers or covered him or her.
Bills, such as electricity, water, heat, cable TV, phone, or others that show both you and your spouse's names.
Jointly-filed Income tax papers (both your names).
An identification card that shows that shows a common address.
Membership cards for video clubs, grocery stores or similar businesses, that show joint membership.
Any other documents that prove your relationship.
Then while that is processing which should take about 8 to 12 months, you would get a receipt from USCIS extending your green card for 12 months. You would continue with your divorce. In the divorce you can ask for whatever custody you want, but the court will most likely decide what is in the best interests of the child. If you will move outside of the U.S., you could eventually lose your green card. You can maintain it for most likely up to 4 years by applying for Re-Entry Permits on form I-131 which would give you up to 2 years each time, but after the 2nd Re-Entry Permit that you get, they get harder to get and they only give it to you for 1 year at a time. Eventually you will need to live in the U.S. or you will lose the status. If you do decide to stay in the U.S. and you do not win full custody (the norm is to have shared parental responsibility and shared or joint custody with one parent being the primary custodial parent that usually ends up being the mother), you would have visitation rights. Often it is every other weekend and one day during the week each week. This can be modified, of course. But if you decide to leave the U.S. and live outside, primary custody would most likely fall to the mother and you would usually get summers and every other holiday season or something like that and that usually would be when the child get older as it may be difficult for the child to travel while young.
Regardless of what happens, as long as you are a good parent, not a danger to the child, you should get joint custody even though your child may not be primarily living with you. You would have full say in decisions about the child.
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