All of the plants you mentioned, in my experience at least, will get quite leggy and flower sparingly in only 3 hours of sun.

Off the top of my head, some that should do well, provided they are winter hardy in your zone (I'm in 7), are Japanese anemone, snakeroot (cimicifuga), great blue lobelia (lobelia syphilitica), perhaps goatsbeard. Somewhat shorter would be cardinal flower (lobelia cardinalis) and astilbe.

There are some shrubs that do very nicely in shade, if they would be suitable. Some flower, some have nice fall foliage color or interesting bark in winter, some evergreen.

There are many factors to consider: Is this constant and dense shade, is it cast by a building or by evergreens or dappled shade cast by tall, deciduous trees with an open canopy? is there bright ambient light in the area? dry or wet soil?

It's in an area under an apple tree and there is a fence which further complicates matters.

I do have a goatsbeard, and am kind of meh about it. I already have a ton of astilbe, so I was looking for something different.

Most on that list are ones I've ruled out since I'm trying not to have plants that are poisonous to children (snakeroot, lobelia). The Japanese anemone is a good idea though that I'll have to look into (they're lovely!). Can you give me an idea of how long they bloom for?

Do you let your children eat plants from the garden? The vast majority of common garden plants are toxic to some degree so having that as a restriction is unnecessarily limiting. In most cases, you have to consume a great deal of the plant to cause any sort of negative reaction and IME, most kids are pretty adverse to eating any sort of vegetation :-) I'd just avoid any that are notablyy toxic - castor bean, monkshood, oleander, etc. or any with enticing berries. FWIW, child poisonings from eating ornamental garden plants is pretty rare and folks have been gardening with small children for centuries. Never was any issue with my three :-)

Cimicifuga (Acteae) is a great choice and with fragrant flowers. Ligularia can get quite tall as well and the yellow flowers brighten a shady spot. I'd suggest foxgloves too but since you want to avoid any toxicity, maybe skip that. Many meadowrue (Thalictrum species) are very shade tolerant and can get quite tall.

Thanks for the recommendations!

My daughter just turned 3, and we do talk about how she's not allowed to pick plants and that we never put them in our mouths, but until she gets older I still am trying to avoid plants with a poisoning risk (just for the fact that if something did happen because I knowingly had planted something known to be toxic, I couldn't live with myself). I usually look them up and do have some plants which have side effects of vomiting or stomach upset, but avoid any that may cause problems more severe than that when eaten,