somewhere on this forum is a cool picture of how someone used Lamb's ear near their pool. Maybe that would give you an idea. I found it by searching "lamb's ear"

lamb's ear is the easiest to keep from flowering...

the mounding artemesias are nice as well, and are sturdy enough for your area. there's also the option of something like ice plant which doesn't flower during the summer...

maybe ant-pollinated plants, and see what natives you might have that don't attract bee.

I think the flower stocks on lamb's ear will definitely attract bees.

they do, mary- if you let them put out flowers.

I think they're hideous looking, so I cut the whole stalk off at the base the minute it shows buds.

there is a non-flowering lamb's ear, I got some from my neighbor-- in 15 years no blooms. but don't know what its called and he's moved.

nearby there is a historical estate that has a pool surrounded by a 'lawn' of mint that is mown reqularly
to keep it short (2"). the effect is great walking across
the mint to the pool.

grasses don't bloom (in the typical sense) have you considered them? You could do a mixture of short clumpers?

or what about some of the prostrate junipers?

diggerb

The flowerless lamb's ear is Stachys byzantina 'Silver Carpet'

Here is a link that might be useful: 'Silver Carpet'

Have you ever thought about Synthetic Grass? That would be perfect to cover that area and soft enough for the kids. If you would like samples contact www.turf-usa.com i did and they sent me samples and i covered a large area with there Elite Fesque, it looks great best thing i ever did in the yard.