Welcome to the Wefugees Community and thank you for sharing your question.
I assume, the reason that you haven't received an answer so far is due to the fact, that our platform and our experts are based in Germany and we are not really familiar with the US immigration rules and regulations.
Therefore, I would recommend you to get in contact with refugee/legal counselling organisations in the USA, for example this one.
However, if you and your partner are recognized refugees in Spain, you are most probably not allowed to "use" the Russian passport anymore. Instead, you can travel with your refugee passport now. Within the EU, you can travel without any visa. But I am pretty sure, that the USA require a visa application, as it is the same for European citizens.
All the best,