1) As I know Family law in the US ties the opportunity to file an alimony and divorce suit to court with required residence in territory of the state.

2) If you will sign a contract, this contract will be obligate to you independent from your place of residence.

3) If the decision of the court about the action of alimony exaction is completed in the territory of one of the states, then reconsideration of this case is not required. In this case you have to present the decision of Russian court to performance to the appropriate court of the USA. The decision of foreign courts must be compulsory performed, if there are no disagreements between the rules of national and foreign laws.