Article 3 of the Hague Convention on the Civil Aspects of International Child Abduction, from October 25, 1980 states that removal or retention of a child is unlawful when:

a) it is in breach of rights of custody attributed to a person, an institution or any other body, either jointly or alone, under the law of the State in which the child was habitually resident immediately before the removal or retention; and

b) at the time of removal or retention those rights were actually exercised, either jointly or alone, or would have been so exercised but for the removal or retention.

Breach of rights of custody mentioned in “a)” may either arise by law, judicial or administrative resolution, or as the result of a lawful, legally enforceable, contractual agreement between the parties.

According to the terms of the Treaty between our countries, one party may deny compliance with legal request of another party, if such compliance is contrary to legal principles of the country that denied the request.

So, there is a very big chance that the Russian court will not take into account the decision of the American court. Since your children are citizens of Russia, they also can obtain a registration in there county of residence. For a Russian court that will determine this case’s outcome, one determining factor will be the conclusion a social agency from the district where the children resides.

You have the absolute right to participate in children's life, even if they live with your wife. Therefore you need to file new action in court of your country, and ask the judge to prohibit traveling abroad for children. Your children are Russian citizens, so, your rights will be violated, because there is no mechanism to make your wife to return the children from Russia.