I think you will have to experiment a bit to find something that might work...
Here was another site with various options. But lets be frank about this: none of this tastes like milk!! It is some watery substance that is flavored with something!
www.organicauthority.com/eco-chic-table/...non-dairy-milks.html
I personally find that the oat milk tastes better than the soy and rice milk from woolies, that is what we buy for now. But, still... yuck! I sometimes mix it with turbokidz shake for a bit of a "treat" like the closest thing to a milk shake! Shame, poor child.
I have started to use "coconut oil" instead of butter in certain recipes which calls for small amounts of butter with great success. I always have a variety of ice lolly pops in the fridge that is dairy free. I make a good one with banana and coconut milk and peanut butter/almond butter - it is really good!
Hope you find something that works for you! I know how painful it is to cut out something like dairy for a child. Really heart breaking.