Mostly shaded and a narrow bed: maybe some lobelia, impatiens or lily of the valley. You could call the garden hotline and see what they say. (206) 633-0224
They've been great for me.

Here is a link that might be useful: seattle tilth

For veggies, you might want to consider something that will grow quickly thus reducing the need for long days in the sun. Possibly radishes or there are some lettuce varieties that can be harvested in less than 60 days.

Impatiens come in many colors and thus would brighten the area. You can plant them 6" from the wall and they will appear to climb the wall. Lily of the Valley is a perennial and should come back every year.

How many hours of sunshine do you have? If at least 4 hours of direct morning sun you can grow a lot of things. Greens tolerate part shade rather well, though everything takes longer to mature to harvest.

Are they attending year round or only until mid June? That affects what you plant. You want 60 days to harvest if you want them to see it.

I'm familiar with working with kids & 2 yr olds aren't going to stay on task very long. They also will step in the beds. Give them a spot for their feet. Practice walking on the path with slow feet before you plant anything. My sister did better with her toddlers using large containers on a table top. She put the seeds in a shaker & of course they over planted, but it was fun to snip the extras away. It might also be helpful to put up a short wire fence to keep their feet out. They're usually on rolls at the hardware store in green or white. A family might have one to lend you.

Use terms like covering feet (roots) with the blanket (soil). Seeds go in the dark under soil to surprise you later (sprout). No peeking on surprises. That may help them not dig down to check sprouting. They understand that.

Plant what you think they'd eat. If you plan to make soup or stew they might eat anything you put in the pot. The stone soup story is a good one & fun to use.

It will be easier for kids to plant larger seeds like beans or squash, but it's too cold for those crops now. Try these:
edible pod peas (can sprout inside & plant out, but the sprouts are fragile)
nasturtiums (later on when soil is warmer)
onion sets - for green onions
potatoes - buy short season like Cherry Red or Yukon Gold & harvest as baby potatoes after you see flowers
calendula (pot marigold)

You could also make your own seed tape gluing the seeds to an unfolded napkin or toilet paper. You can look up online more about using seed tape for planting. My kids liked to do that inside where it was warm & then we'd get proper spacing outside in the cold. Carrot seeds are too tiny & take too long to sprout for little ones. Buy the carrots to go in the soup & you'll be glad you did.

Otherwise plant transplants of vegetables they'd like to eat. Right now lettuces & pansies are perfect. Pansy flowers are edible & pretty in salads or in a sandwich. They don't have much flavor, so toddlers might eat them. They also might like chard or spinach.

Carpinito Brothers in Kent has an amazing assortment of cool weather plant starts for $1.10 with 4-6 plants in each. They also have warm season vegetables that need protection, so be sure to avoid purchasing them such as tomatoes, squash, beans, & cucumbers. Even broccoli may go to seed this spring if we have a cold snap when the plants are larger. If your area is protected somewhat you can transplant broccoli now. You can ask a worker to help you select the things that can be planted out now.

Strawberries might be a lot of fun for them, but won't harvest until June. I'm southeast of Seattle, so don't pick strawberries until late June, but you might have them earlier in the city. Skip bare root & plant already potted strawberries at the same depth as the pots. Look up how to plant the crowns so you know what is too deep or what is too high. They're tricky.

Herbs are fun to give haircuts. Chives or oregano tolerate a lot of snipping. Be sure to read up about how to harvest chives since you harvest the whole blade not just the tips.

Be sure to bait for slugs. Have a plan to keep out dogs, digging cats, pigeons, or pedestrians if any of those could have access to your garden plot. An upside down wire basket staked might work well in your situation or bird netting on stakes that are topped with upside down water bottles to support it. Of course, you remove the netting each time you tend, but can water gently through the netting.

I wish you the best & applaud your effort of working with little ones in the garden.
Corrine

Sugar snap peas may grow in a semi shaded area. The seeds are large and the kids like eating the tendrils as well as pods. Kale can be started in paper cups -3 seeds to cup and they can pick out the biggest plant to keep and snip off the others. Lettuce now comes in pelleted seeds so easy for little fingers to count out 2 seeds per hole. Do not discount the fun factor for the little ones when they discover the worms, snails centipedes, colored rocks. They are learning and exercising their fingers and eyes. Alpine strawberries are another good plant because they never stop producing. Just a few days ago when working with daycare kids, they were eating chives and then discovered that they could design edible jewelry from the chives!!!! That was the end of pulling weeds and preparing for planting potatoes.
Do check that there is no lead or other toxic stuff near the building where edibles would be grown. If in doubt use containers and safe potting compost.

Lily of the Valley is poisonous. It has red berries which children might be tempted to eat. It can also be a garden thug.

And lily of the valley takes over unless constantly policed.

Yep, Walter used Lilly of the Valley to poison Brock in an episode of Breaking Bad.

For flowers, I'd recommend columbine (Aquilegia formosa), scarlet monkey flower (Mimulus cardinalis), cardinal flower (Lobelia cardinalis), and Oregon iris (Iris tenax). These are all OK in limited sun and moist conditions (kids love to water, water, water).