There are several spots where you can park quite safely IMO. Great Blue Heron Reserve is a good spot to park, take the kids through the reserve and see the birds etc, then walk to the river via the trail. There should be some kid-friendly spots at the trail head once you reach the river.
The safest spot to park IMO is the dog park and new playground just downstream from the Vedder Crossing on the north side. That playground is great for kids, there is also a pretty awesome food truck at the lot usually. The dog park is used constantly during daylight hours so you have all the security needed. I'd walk downstream on the Rotary Trail to find spots. You may need to walk down to Peach Road to find kid-friendly spots.
As Ralph said, there's nothing wrong with targeting newly released juvenile hatchery steelhead in July and August, as long as the participants are well aware of wild fish and practice proper catch and release when these are encountered.