My question is what you're actually using the rice milk for. If it's in cooking, different plant milks handle differently and you should experiment with making them and see what works well in different recipes. Home made almond milkis lovely and you can dry out the residue and use it as almond meal llater . If you're getting your child to drink a glass of milk or a smoothie, consider ditching the milk substitute and getting them used to drinking other things. There are better ways of getting calcium, etc. than what is artificially added to a lot of commercial non dairy milks.
My background is that milk was identified as not good for me when I was about six. I didn't really like a lot of the milk drinks that my parents tried to get me to drink instead so in the end I just went without and have never really felt deprived. I drink my tea or coffee black as that's how I have always had it. I occasionally make a non dairy milk from scratch if I think a recipe needs it, or use coconut milk or cream as a substitute, but it's not a commonplace event. My bone density is fine (and has always been fine). Just some food for thought.
There is lots of good food out there that has no dairy at all. Take heart!