You're both lucky. My son couldn't tolerate cow's milk, soy milk OR rice. At least your children can drink
something. We were stuck with the hypoallergenic milk (and its cost) for ages. All outgrown so I hope that's your stories too!
Be careful in Singapore. I used to live in Hong Kong and went to SIN a lot. I have the lactose problem (different) but I still can't do dairy. Some of the soy milks do have whey or milk added for taste. I found out the hard way so you don't have to!
Check the label.
There is nothing inherent to soy milk that would exempt it from the same rules that apply to cow's milk. The most important point is that it is for your
children. That's what they'll need to know and you may want to add the fact that you have checked with the airline and they do not have soy milk on board. Show the doctor's note and any email you have from ANA as you go through. If anything starts to get sticky, ask to see a supervisor before things get heated.
Good luck!