You should treat adopted children in the same way that you treat biological children. This includes your actions when you are going through a child custody matter. You shouldn't do anything that will make the adopted children feel like they are unloved or unwanted.
There are some special considerations that you have to think about when you are going through this situation. One important point is that the adopted child might have to get some extra support during the process. This isn't always the case, but it might be necessary if the child is old enough to remember the time in foster care or the adoption.
You will need to come up with the child custody agreement for these children, just like any other child. This should include points about visitation, education, medical care and other points you find important.
It might be possible for you and your ex to go through mediation to come to the terms of the custody agreement. For many people, this is beneficial so that you don't have let the court decide what is going to happen. You and your ex can take your child's needs into account.
You know the challenges that your adopted children have. Throughout the divorce process and as the child learns how to navigate the new family dynamics, you should take the time to make sure he or she is adjusting well. Adopted children might guard their feelings and thoughts so this might be challenging but knowing that you are there for them no matter what might help the children.
Source: Our Family Wizard, "Co-Parenting an Adopted Child," accessed March 09, 2018