LOGAN, W.Va.—When Bobbie Lou Moore goes to the polls here Tuesday, she will vote for candidates who she thinks can best deal with the region’s opioid crisis.

The 44-year-old has taken in two children, one 16 months old and the other 3 months old, who were born addicted to opioids. Their mother is addicted, their two grandmothers were jailed on drug-related charges and one of their grandfathers died of an overdose, she said.

“Everyone...