Investors in the high-end denim brand Imogene + Willie are trying to force the Nashville, Tenn., retailer into bankruptcy, accusing the founders of misspending company money on luxury clothing items, spa visits and home renovation projects.

In court papers, investors asked a bankruptcy judge to replace Imogene + Willie founders Matt and Carrie Eddmenson with new leadership, saying the couple spent a $1.5 million cash investment “on themselves to support a lavish lifestyle of personal indulgence while failing to meet any of...