Well,
They can't fall out of the sides because there is enclosure on the sides (you step down into the log when boarding).
In front of you is a padded bar that you can hold on to.
Also, really no part of the ride will require you to hold on your child. From the outside it looks worse than it is.
The drop is not as steep as it looks and it's very quick from beginning to end.
Even some of the dips in the ride are so mild that you likely will not have any reason to have to worry about "holding them in".