Translation:Kateřina eats pears often, while her husband cannot stand them.
"Kateřina often eats pears, while her husband cannot stand them" is among the accepted translations. Duo should recognize the contraction automatically, and the sentence with "can't" does test correctly. If that is exactly what you wrote, you may have been bitten by the Duo grading bug.
I am not sure I understand your question, so this may not help But její muž nesnáší means "her husband can't stand," and it does not indicate what he can't stand. So je here means "them," that is, the pears. If this isn't helpful, please try asking your question again.
You could use "hrušky" again. Otherwise, no, the only possible pronoun is "je".
Check out the declension of "ona" here: https://en.wiktionary.org/wiki/ona#Czech
(Another accusative form is "ně", but that's used after prepositions - e.g. "Kateřina chce koupit hrušky, takže pro ně musí do obchodu.")