When Bode Miller, the Olympic ski star known for daring Alpine racing, met Sara A. McKenna in San Diego last year through the high-end matchmaker Kelleher International, they were both professing interest in finding a marriage partner, she recalls.

The relationship did not last long — but she did become pregnant. And now the skier, 36, and Ms. McKenna, 27, a former Marine and firefighter who is attending Columbia University with G.I. Bill support, are locked in a cross-country custody fight that has become not only tabloid fodder but also a closely watched legal battle over the rights of pregnant women to travel and make life choices.

In December, when she was seven months pregnant and already sparring with Mr. Miller about their future relations, Ms. McKenna moved to New York to start school. Mr. Miller accused her of fleeing to find a sympathetic court, and a New York judge agreed, castigating Ms. McKenna for virtually absconding with her fetus. This allowed a California court to subsequently grant custody of the baby, a boy, to Mr. Miller and also set off alarm bells among advocates for women’s rights.

But on Nov. 14, a five-judge appeals court in New York said Ms. McKenna’s basic rights had been violated, adding, “Putative fathers have neither the right nor the ability to restrict a pregnant woman from her constitutionally protected liberty.”