Recommended Wall Mounted Battery powered Reading Light for 2 year old child?

I’d suggest this Solarforce lens Solarforce "close-up" convex lens

that thread lists a HK source

It gives a lovely smooth flood.
Then put a hang point above child reach and just bring the light in and out with you.

That way if you find the kids have any trouble getting to sleep you can easily use a non-blue-light source for the evening reading (amber LED or just yellow filter film on the light)