I have two children adopted from Ukraine. There was (and is) no "finalization" that needs to take place in the U.S., unless the children come to the U.S. on an IR4 visa. When you bring a child to the U.S. on an IR4 visa, you already have full, permanent, legal custody of the child. The child's passport has been redone to show you as the birth parent. Readoption in the U.S. is required solely for U.S. immigration purposes, to convert the permanent residency to proper citizenship. Even on an IR4 visa, the child is already yours before you step foot back into the U.S.
However, when a child travels on an IR3 visa, no readoption or finalization is required. The child becomes an American citizen upon setting foot on U.S. soil by action of law. Many parents choose to readopt (or have a formal "Recognition of Foreign Adoption" judgment) in order to get a U.S. birth certificate, change the child's name, or comply with state laws. As far as the U.S. itself is concerned, the child who arrives on an IR3 visa is a citizen.
None of this is particularly significant, however, since the child must have been adopted in the home country before either an IR3 or an IR4 can be issued. Adoption in Russia is exactly the same as adoption in the U.S. as far as the legalities go. There are no do-overs, RMAs, or easy outs if the child turns out incompatible with your family.
My heart goes out to all those who have adopted or given birth only to find that the child has severe emotional, physical, or psychiatric problems. RAD, ODD, ADHD, and other acronyms are very, very familiar to anyone who adopts -- especially an older child.
Being lied to by the agency or orphanage is, unfortunately, par for the course. It does not change the parent's responsibility. The agency and the orphange workers did not go before a judge with a petition to adopt. The agency did not accept custody of the child. All adoptions are essentially independent adoptions, despite what an agency or orphanage may say. The legal obligation is entered into by the parent, and approved by the judge. You cannot undo it by claiming false advertising or damaged merchandise. From the moment the judge bangs the gavel, the child is yours, with all the rights and responsibilities pertaining thereto.
Both of my children have post-institutional behaviors, and neurological problems caused by lack of nutrition in early childhood. They also have emotional and behavioral issues, neurological deficits, and suffer the (often life-long) effects of neglect and abuse.
If I were ever to decide they were too much for me to handle, or threatened the rest of the family, my only recourse would be to seek hospitalization, intervention by social services, private placement somewhere, or getting someone else to adopt them. They are my kids, just as surely as if they'd been born to my wife. I cannot return them with a note.
(I'll mention for the record that I am speaking theoretically about getting rid of my kids. Despite their problems, they are wonderful, and we are a happy family. The first year was very difficult, and the younger boy will probably never be fully independent, but I wouldn't even consider life without them.)