Council members Hammond, Spielman, Russell Weaver and Matt Ryan voted 4-0 to appoint Gale, 48, of 109 W. Main St., to the vice mayoral post.
Troxell was appointed by a 4-1 vote, with Spielman casting the dissenting vote. Spielman said after the meeting that he voted against the appointment because he thought consideration should have been given to Earl "Gene" Benner Jr., who lost his bid for election to the Town Council last November.
Councilman Don Kable was voted out of office in the November election.
Troxell is the fourth woman to hold a council seat in Sharpsburg, officials said. A widow, she has lived in Sharpsburg since 1993 with her sons Sean, 16, and Alec, 14.
"I'm good at understanding what people are saying. I hope to be a voice of calm listening," Troxell said.
Troxell, 42, of 114 S. Mechanic St., said she volunteered for the council seat because she thought she could help.
After teaching language arts at Boonsboro Middle School for one year, Troxell left teaching because of a heart problem that requires her to get a double lung transplant, she said. She has been on permanent disability since 1991.
At the age of 30, a hole was discovered in her heart that had been there since childhood, she said. While the hole has been fixed, it had damaged both her lungs.
She has been waiting for a lung transplant for 20 months, she said.