The eldest daughter of former US vice president Dick Cheney, who’s been embroiled in a bitter rift with her lesbian sister for not support equal marriage, has abandoned her campaign to become a Wyoming senator.

“Serious health issues have recently arisen in our family, and under the circumstances, I have decided to discontinue my campaign,” Liz Cheney said in a statement on Monday. “My children and their futures were the motivation for our campaign and their health and well-being will always be my overriding priority.”

Her campaign had been overshadowed with claims that she had parachuted herself into Wyoming as a state outsider.

Since last summer, she has struggled with a series of setbacks.

A public spat with her lesbian sister, Mary, over same-sex marriage dominated US national headlines for several days in the autumn and winter.

Mary Cheney condemned her older sister in September for not supporting marriage rights for same-sex couples, leading Liz Cheney to say in November that she believed in the “traditional” definition of marriage.

The remarks prompted sister Mary Cheney to post on Facebook: “You’re just wrong.”

“Liz – this isn’t just an issue on which we disagree – you’re just wrong – and on the wrong side of history”.

Mary Cheney posted a quote from her wife, Heather Poe, saying that the elder Cheney sister “didn’t hesitate to tell us how happy she was for us” when they wed last year in Washington DC.

“Liz has been a guest in our home, has spent time and shared holidays with our children,” Ms Poe wrote. “To have her now say she doesn’t support our right to marry is offensive to say the least.”

The rift received public attention again in December, when Dick Cheney appeared to take the side of his eldest daughter.

“We were surprised that there was an attack launched against Liz on Facebook, and wished it hadn’t happened,” Dick Cheney said in muted comments at the National Press Club. “It’s always been dealt with within the context of the family and frankly that’s our preference.”

Unlike many Republicans, Dick Cheney himself said in 2011 “he didn’t have any problem with” same-sex marriage.