Hello!
I've never ridden an elephant before. But I do agree it is a must do even just once in your life. As far as I know, regarding the issues of maltreatment, the elephants are being treated better now. In the past, they would carry up to five passengers. Now, the limit has been two passengers plus the driver. They are also limited to just five trips in a day. The government also does routine inspections to make sure that the elephants are of great health condition.
You can even create paintings on the elephant using paint and bamboo sticks. I think that can be a fun activity for kids. Of course, you can take many pictures as you'd like as well. Just being able to ride the elephant from its trunk is quite cool too. At the end of the journey, you're supposed to wash off the paint from the elephant with water. That's quite a cool experience as well.
Like you said, it's recommended to visit during the earliest time possible. Lots of tourists flock for the elephant ride and you might line up for long if you're late. Bring your own water especially during the summer season as it can get really hot.