What part of the country do you live in?

Chicago.

With the winter we had this year, it's a wonder that anything grew back! I would suggest planting a little bit closer to the grass and away from the driveway to try to avoid winter rock salt/winter melt runoff. Have you tested your soil? Some other low-growing, flowering shrubs and perennials that need less sun than potentilla include compact spirea, astilbe, and heuchera. Look around your neighborhood to see what others are growing successfully in part-shady areas and talk with the folks at a garden center for other suggestions. There are lots of ground covers that like part-shady areas, but if you aren't careful, they'll end up in the lawn! For now, you might consider planting colorful impatiens, which are annuals that do well in shade.

Hosta and Bleeding Heart survived our NE weather!

Coral bell comes in several colors and they do well in morning sun and shade. They come in a purplish color that is very attractive. They should come back year after year but the location near the driveway will be an issue as the previous commenter pointed out
Good luck!

Thanks!

I had some coral bells in there, and they did come back... but something ate most of them! (We've had slug and caterpillars in bunches this year). My wife is averse to Hosta for some reason, but I think they are a strong candidate.

My neighbor has had success growing azelia in a similar spot across they street, but they get a touch more sun on on the east side of the block.

I would do a cool variegated hosta inter planted with ferns and bleeding heart and/or astilbe. I also love Lenten rose in my shade garden.

I'm in Milwaukee, also Zone 5. I'd recommend alternating hostas and Color Flash astilbe. Both are shade lovers, and the color flash astilbe flowers pink with foliage that changes color in spring, summer & fall.

Houzz won't let me attach pictures at the moment. I'll try again later.

I vote for astilbe. They're shrub-like until their feather-like flowers bloom.

That's not a great place for a bed. It's too disjointed--not attached to anything else. Plant grass and stop worrying about that thin space.

I question having beds along your driveway. You live in a snowy region and if you have someone plow your drive or remove your snow yourself, you will likely pile snow on anything planted there, or plow over the area. Instead, plant grass to the edge of your driveway. And expand your beds closer to your home, safe from plows, shovels, and salt application! (I live in NE Ohio and know about snow removal issues!). Good luck!

Another vote for hosta. For flowers, the blue / pink hydrangeas are pretty and showy and prefer shade. There are some sun loving hydrangeas too, so ask at the garden center. Also, some can get large, so look for smaller growing, easier to contain varieties.

I agree with all the suggestions about good plants but I have to say in reconsidering I would just go to all grass there.

I live in Iowa and have had great success with Hosta's. They come in many variations and sizes.