We are a British family at SAIS, and we are delighted with the school. It is quite demanding - academically, but also behaviour standards, sport, drama (proper competitive teams & tryouts from grade2/UK yr3). But I think that is likely to be less of an issue for tiny ones!
The school is big, but the pre-K area is separate and has its own play area. And the campus itself is amazing, I had looked at many of the schools in Singapore as well as some pretty good independent schools in the UK and I have never seen anything like it!
The culture is quite international, which we like - may 10-15% Brits, half from N America then a good mix. I think they try to get the same national mix of teaching staff as amongst the pupils. Obviously it is predominantly US in terms of the feel of the place, but the curriculum is IB with a real focus on maths, which we were attracted to. And we love the IB, the kids find it really engaging, and the school pushes the maths & spelling, which I think is sometimes seen as a weakness of the IB. I have one eye on the British curriculum but am happy my children are covering the essentials and more. And the daily mandarin is great, my son has little chats with the taxi drivers here 
Overall, the school markets itself well but in our experience, lives up to it. The staff seem dedicated and happy, and the children do too. Choosing a school is a very personal thing, but we have been really pleased with our choice.
Good luck with the move!