Nothing like the trample of little feet to kill off that lingering ivy! I would not use pea gravel though, that seems a bit harsh for bare knees. How about some plain wood chips?

Shade areas are tough to grow flowers in. Several of the things you mention likely go dormant in the summer (not a bad idea if kids are more apt to run around in the summer). Good native perennials include ferns which tend to be very forgiving. Solomon's seal is nice but it has berries if it flowers and you may not want something that tempts.

Tough native shrubs include Virginia Sweetspire (Itea virginica) and Clethra. They both sucker a bit and so are more likely to recover from any "accidents". Viburnums and Aronia are also good candidates for that reason.

I have to repeat that depending on how much shade you have, you may not get as many flowers as you'd like on these.

Hope that helps! Good luck.

I second the no gravel in a kids' play area. My son tripped and fell on gravel and a stone went right into his forehead...needed stitches. For play in shade, I'd use a shade tolerant grass around the places kids play, maybe with playground mats where they might fall, and a nice garden on the perimeter. Kids like to hide in bushes, too, so maybe a forsythia that can be pruned to allow for that, would be fun.