Of course, since your first child's name was named after a beloved Uncle, you could name this child after someone beloved on your side of the family! It still fits a theme, even if the theme isn't Russian.
Otherwise, other Russian names that aren't too uncommon to Americans, or have ties to common American names include:
Natasha, with the nicknames Nat or Tasha. Felixa (nickname could be Lexa) is the female form of Felix, which is also seen in Russia, and is a form of Felicity. Anastasia is also seen in Russia, with the down to earth and approachable nickname of Ann or Anna. There is also Alina, Alla, Elena, Vera, Veronika (Veronica), Viktoriya (Victoria), Anzhelika (Angelica), Natalia (Talia), Elizaveta (Elizabetha), Eva, Inessa (or Vanessa), Izabella, Klara (Clara), the list can go on. Try this index of Russian girl names. There is also Arkady, which is commonly a boy's name, but I think could be a girl's name too, since it sounds more feminine to me.
Natalia isn't obviously Russian but it is. Your Russian relatives could call her Natasha for short.
I also like Clara. I read a book where the Russian heroine was named Emelia, but I am not sure how accurate that was.
Lara or Larisa (the long form)
Anna (actually very Russian and not obvious at all)
Zoya (Russian form of Zoe)
For boys I like Nicholas. It maybe too popular but it is Nikolai is the more Russian form. Nicholas is an American form.
I happen to like Boris, but it may be too over the top.
Mikhail form of Michael( maybe too close to the popular Michael)
Peter (probably a translation but often used when referring to the composer of the Nutcracker)
Leo (as in Tolstoy)
Sebastian/Sevastian (my own current favorite, and in Russian the V and B are switched.)
Stepan (Russian form of Stephen close to Stefan/Stephan)
I hope this helps. Good Luck!
Ok, sorry for any repeats...
I LOVE Tatiana
Parisa (Farsi, but it might work)
Donya (also Farsi... ok, into Russian gear)
Karenina (just for the literary reference)
Kallista (Love, love, love, love, love, love)
Milena (love love love love love)
Misha (love love love love love)