I don't think there is any way to predict the condition of the battery you will receive. I recently acquired a second generation iPad and considered giving it to a 9 year old. But thinking it through, the old iPad no longer runs the current version of iOS. It no longer receives iOS updates. It probably doesn't have good battery life any more. And it's going to be slow compared to newer devices. I decided to get a 6th gen iPad instead. It cost more, yes, but I know the condition and it will last many years.
If you can't do that, then I'd just go with the used iPad. Who cares if the battery is bad? If battery life limits your 3 year old's screen time that might be a good thing. Otherwise, they can use it while connected to a portable power bank that you buy for $10-$20.