Ask Mr. Smarty Plants

We don't seem to have enough information to answer your question, so we'll do some speculating. You have to figure out what is different between the two beds. Does one have more shade than the other, or less opportunity for irrigation or does water sometimes stand on one bed and not the other? If we understand you correctly, all the plants you named started out in both beds. In the Spring, 2 plants, the oenethera and the yarrow, didn't come up in the north bed. It's not that the plants in the north bed migrated, they just failed to re-emerge in the north bed when Spring came.

Good in the south bed but not in the north bed:

Oenothera speciosa (pinkladies) - needs full sun (6 or more hours of sun a day) and moist soil, native to your area

Achillea millefolium (common yarrow) - sun or part shade, can withstand dry soil, prefers moist, native to your area

Good in both beds:

Sedum ternatum (woodland stonecrop) - sun or part shade, moist soil, native to your area

Iberis sempervirens (Candytuft) - full sun, native to Africa, Asia, Europe

Lavender - native to the Meditteranean area, likes dry, sunny area

It looks to us like there was/is more shade than the plants that failed to come up in the north bed could withstand. Since the Lady Bird Johnson Wildflower will only recommend plants native not only to North America but to the area in which the plants are being grown, we will find some native blooming plants that are okay with part shade (2 to 6 hours of sun a day) or shade (2 hours or less of sun a day.) You can follow each native plant link to its database page to learn about its culture, light requirements, colors and so forth.  If both beds have full sun, you will have to examine other factors that might be different, going back to Recommended Species, clicking on Virginia on the map, and then selecting herbs (herbaceous blooming plants), perennial in Lifespan, sun in Light Requirements, and then Narrow Your Search. If you wish to change the Light Requirements or put in the soil moisture, that will narrow your choice down even more. 

Herbaceous Blooming Plants for part shade or shade in Virginia:

Aquilegia canadensis (red columbine)

Asclepias tuberosa (butterfly milkweed)

Caltha palustris (yellow marsh marigold)

Campanula rotundifolia (bluebell bellflower)

Conoclinium coelestinum (blue mistflower)

Coreopsis lanceolata (lanceleaf tickseed)

Gentiana clausa (bottle gentian)

Iris versicolor (harlequin blueflag)

Lobelia cardinalis (cardinalflower)

From our Native Plant Image Gallery:

Oenothera speciosa

Achillea millefolium

Sedum ternatum

Aquilegia canadensis

Asclepias tuberosa

Caltha palustris

Campanula rotundifolia

Conoclinium coelestinum

Coreopsis lanceolata

Gentiana clausa

Iris versicolor

Lobelia cardinalis