In her youth, Stella was fully aware of Harry's flaws and overlooked them amiably. In later years, she was rather shrewish with him and often criticized him for his drinking, overeating, and carousing.
In the 2250s, Mudd said he tried to win her approval by buying a moon with borrowed money, which convinced her to stay with him. He was later captured by Klingons while trying to flee his creditors, but vowed to escape and return to her. (DIS: "Choose Your Pain")
In reality, Mudd had tried to escape Stella herself. The crew of the USS Discovery determined this after Mudd's countless attempts to steal the vessel in order to sell it to the Klingons. Once the crew had deduced this, they contacted Stella and her father, who came and took Mudd. (DIS: "Magic to Make the Sanest Man Go Mad")
Sometime before 2268, Stella became separated from her husband when the latter resumed his career as a con artist. Mudd later created an android replica of Stella that was programmed to shut down on command so that he could always get in the last word. His revenge backfired on Mudd when James T. Kirk commissioned at least 500 copies of Stella Mudd to serve as parole officers for Harry Mudd on Planet Mudd - none of which responded to Harry's command to "shut up". (TOS: "I, Mudd")