Dear Millie1,
Singapore resident here!
Residenced Apartments are really good here if you have more than one child, though check that they do stopovers. Treetops on Orange Grove Road is lovely (2 bed flats with kitchen), Great World City Apts on Kim Seng Walk also v good, as is the Ascott.
Due to long term stay, have not experienced any of the hotels. The Sentosa Resort is beautiful but you're right, it is a bit of a way out when you are in a taxi with 2 little ones. Sentosa is linked to Singapore by bridge. Underwaterworld is a great aquarium, and nice and cool inside for the baby. The hotel should have a bus that ferries you around? Siloso beach is the best, and there is a good bar called Coastes on the sand. The beach is very hot and sticky after 10 and before 5, especially for a baby.
Singapore is a very child friendly place imo. BUT MRT is not good with pushchairs (have been on it ONCE in 3 years) but then taxis are dead cheap. (you need your rockatot carseat for the baby, but your 3 year old can probably just go into the seat belt).
Night Safari is great for jet lagged children, but the zoo is very hot after 10am, especially coming straight from winter in the UK, but it has got a good playground with a waterplay area.
Tanglin Mall, on Tanglin Road has an indoor play Gymboree and Kindermusic, and a brilliant Aussie Cafe called Cafe Beviamo on the 2nd floor, which does half portions and has high chairs, and will respect nut allergies.
I'll try to find out more info if you need it...