Mission accomplished in the Eurostar, London-Paris-London. I just did a 2-day round trip by myself with Marcelo (3 1/2) and Amalya (7months) and it was as smooth as a walk in the park, sort of, because I booked our seats in the “family wagon”. It a closed coach, with only 4-seaters facing each others, and smaller than usual tables that fold. So there is plenty of space for the little ones to wander around, and the idea is that no-one is allowed to give you the mean look. Plus the baby changing table is just nearby. To book those seats, you need to call customer service rather than booking online.
Bozaround tip: book the seats in Coach 18 as you go to Paris, and in Coach 1 as you do the Paris-London, that way you are among the first ones to get off the train. Quite convenient to beat the taxi line. However, it’s best to reserve a taxi in advance for Paris (try Alpha Taxi+33145858585 or Taxi G7 +33147374739) as there are usually not enough of them in the station. The driver will wait for you just off the platform.