Hey TXboom,
This answer might be a bit late, but I used to fish the Tualatin a LOT when I lived in Tigard. I'm going to guess you're banking it - and you didn't mention how old the kiddos are so I'll assume we're talking young ones to pre-teens, you can adjust accordingly if the kiddos are bigger.
Cook Park and Browns Ferry Parks both offer docks to fish off of - Browns Ferry is limited to pretty much just the dock, and it gets used pretty heavily by kayakers depending on the time of year and if you're fishing on a week day or week end. Browns Ferry is fairly deep right off the dock - used to be at least six feet but my knowledge is out dated - we moved to Texas 5 years ago, who knows how the winter floods reshaped the river since - easy to guage the depth tho if you've got a long enough fishing rod

These were taken from the dock at Browns Ferry.
Used to do pretty well on largemouth and smallmouth here, and my kiddo would catch bass with little more than 12" of line out with a rooster tail or a beetle spin tied on, and walking the length of the dock with the rod tip in the water. Bass dart out from under the dock and snatch the lure.
Cook Park has a boat launch and a dock, and a couple good stretches of bank nearby to fish from. The river by Cook Park is also shallow enough to wade on the park side, for you / teenage kiddos. That opens up more water to fish. If you're fishing from the dock or bank there's still decent amount of water to cast to, but it will get boring after a bit. I focued more on the carp / pikeminnow fishing at Cook Park, but I'd wade upstream and throw flies or lures for bass. Carp fishing is crazy good in Cook Park - and if you want to get your kiddos into some monster size fish, its easy to do there. I couldn't find any pix of the carp off hand, but here's one of a pikeminnow I caught off the dock at Cook Park:
If you're willing to drive a bit futher, the Tualatin has some excellent fishing in West Linn - from Willamette Park at the confluence with the Willy, or up stream to Fields Bridge Park on Borland near where Borland turns into Willamette Falls Drive. There are a number of spots you can hit from the bank at Fields Bridge, be cautious with littles though - the river will run deeper and swifter in this section too. There is a good trail that runs near the river and will get you to the access spots.
Willamette Park has a lot of bank access, and of course you can also fish on the Willamette there as well. We used to fish off the dock on the Willamette, but double check the regulations haven't changed to prohibit fishing from the dock. There's a big L-shaped dock for boats to tie up to, that's the one we fished from.
A little more of a drive, but another good place to fish is Mary S. Young Park in West Linn, you can access the Willamette there and the bass fishing was always good in warm months. There's an island you could also walk out on (there was a connecting ramp moons ago, or you could wade when the water was low) and it has a lagoon on the down stream side that was good. Its a good trek from the parking lot, but way back when in my first marraige - my step daughter made the walk at 5 years old without too much fuss. You'll get your steps in going back & forth, just don't stay too late, the gates lock, and you have to call West Linn PD to get you out if you get stuck after hours. Thankfully they didn't give us too hard a time, or a ticket when it happened to us.
If you want to drive the other way - toward Hillsboro, Rood Bridge Park offers some bank access. I never did great in that stretch for bass though, but I caught a few. Lots of wood in the water up that way. Good bass habitat, but also good lure-stealing habitat.