A slope in my yard is covered in pachysandra and is being overrun with Bishop's Weed. I have spent a great deal of time trying to dig it out, to no avail. I also have ivy in the area and wonder if it might overtake the Bishop's Weed, which I would prefer? I would appreciate any advice you might offer.
St. Clair County Michigan weed issues
Bishop's weed (aka goutweed or snow-on-the-mountain) is a perennial plant in the Apiaceae (Carrot) family. his plant has the ability to form large colonies from underground rhizomes. Leaves are alternate, compound, with toothed-margined leaflets. Some plants may contain white-edged leaflets, but others will be completely green in color. It is usually the variegated form that is cultivated as an ornamental.
As you are finding, control of goutweed can be very difficult, particularly given this location amongst desirable broadleaf plants. Digging up the root system and removing foliate are certainly options for control and will weaken the root system over time, but it could take a very long time.
There are no selective herbicides that will kill bishop's weed and not affect pachysandra and ivy. Depending on how interspersed it is, how big the area is, and how large of a nuisance it is, you could try spot treating with a herbicide such as glyphosate (Roundup® Weed and Grass Killer, amongst others). Products containing glyphosate will injure other plants contacted during application, so some replanting would likely be necessary for the pachysandra and ivy after the bishop's weed is controlled. Multiple applications will likely be necessary for complete control. Glyphosate does not have activity in the soil, so once you are satisfied with your level of control it is safe to replant desired species. Remember, always read and follow labeled directions.