Shortly before marrying her husband in upstate New York in 2000, Tanya Finch began pursuing a nursing degree. While attending school, she worked multiple jobs to support the family, which included a son from a previous marriage and a daughter. Her husband, Kenneth Quarty, was legally blind and didn't work outside the home.

When the couple filed for divorce in 2009, Mr. Quarty said he was entitled to an upfront percentage of all the money Ms. Finch would potentially ever earn as a result of getting the degree. Under New York...