Camp Muir - leaves from the Paradise Visitor Center. ~8 miles, 4.5k of gain, huts at the top. Maxes out at 10k elevation. Permit required for camping (lottery opens in Februaryish?), but May isn't the peak climbing season, so they're usually available whenever.
St Helens - Leaves from the Marble Mountain Sno Park. ~12 miles, 5.5k of gain. 500 permits available per day. May is peak season, first-come-first-serve in Feb. Mother's Day weekend is particularly grand since there's a tradition in the memory of guide Kathy Phibbs who skied it in a dress on Mother's Day after the post-eruption travel restriction ended. You'll need to go dress shopping. You could hit Hood up to illumination saddle the next day.
Ruth - leaves from the Hannegan Pass Trailhead. Similar stats to Helens. Technically has a
Hidden Lake Lookout - Leaves out of the Hidden Lake Lookout trailhead. 8 miles, 3,300 ft of gain for the summer route. Lookout is first come, first serve. Just across from the Isolation Traverse & Klawatti Ice Cap -
beautiful area with a 50 classic climb & 50 classic ski descent. This route lets you leave the technical climbing gear at home.
Mount Ellinor - 6.2 miles, 3300 ft of gain. Olympics might be a gamble by May based on the last 2 years.
Green Mountain Lookout - Leaves from the Green Mountain Lookout trail, 8.5 mi, 3,300 ft of gain.
Birthday Tour - leaves from Washington Pass. Can't recall stats, but probably 4 miles, 2k gain for the main variation. Lots of other options in the area though.
Skiing in the Cascades in spring is all alpine, above treeline, usually steep (Muir's the mellowest and skis like a blue groomer with the exception of a 200ft steep section. Helens is slightly steeper. Black groomerish?). Alpine-ish starts are necessary for the longer/steeper routes, so I'd find a base camp rather close to a base if you don't go the hut route, and finding multiple tours in the zone. Ellinor is the only one that doesn't have something else with similar accessibility right next door. Washington wilderness area coverage makes lodging interesting. Most of these, the closest major hotel chain is an hour away, mom & pop places closer, and in-park lodging or alpine club lodging with a more communal lodging experience (shared meals & chores) within minutes for a few.
If you want something with some glacier travel & guided, Mountain Madness does family trips and I'd recommend requesting Mallorie Estenson, or Lyra Pierotti if Mal ends up on Shasta (she also says put that on your consideration list). What they'd guide for minors totally depends on their experience, but in Mal's experience, their program manager Jaime generally does a good job sussing out a good fit.