Did the same thing in June - even with 2 kiddos preferred Aeroexpress. We ordered a taxi before boarding - there is a phone by the entrance to the Aeroexpress station at SVO - ended up paying 450 Roubles and the driver was waiting for us right on the arrival platform at Belorussian Station.

On the way back we ordered a taxi through Hilton and they charged us 750 for the same trip, but I was too tired to argue.