US rules require US citizens to enter & leave the US on their US passports - if you hand over any other passport you probably will have to explain why you have no sign of lawful entry into the US

So you'd have to show both passports but the Israeli one will get you onto the plane

On the return you'd need proof that you'd be allowed into the US, so you'll have to show your US passport, but then you'd be asked "where's your visa", so you'd have to show your Israeli passport

So the simple answer is that you'll have to travel with both passports and hope the Russians don't decide to be stroppy