If you marry before your child is 18, your USC spouse can petition your child to immigrate as her child; and as long as she petitions the child before the child turns 21, the child will be in the Immediate Relative category with no wait for visa numbers. This will only work for your younger child, assuming you marry before that younger child turns 18. It will not work for your older child who is already 18. You can petition that older child after you become a permanent resident, and that child will be an unmarried under-21 child of a permanent resident in the F2A category which has a wait for visa numbers of around 2 years. But there is a big danger that they will age out before a visa number becomes available, and go into the F2B category which has a wait of around 7 years.
Another option that would work for both children, is for you guys to not marry yet and for your USC girlfriend to petition you for a fiance visa, and you leave the US to get the K-1 visa. Your unmarried under-21 children can get K-2 visas. As long as you and your children enter on K-1 and K-2 before they turn 21, they can do Adjustment of Status in the US at the same time as you do AOS (after your marriage to the USC within 90 days of entry), even if they turn 21 before or during the AOS.
