My cat was abandoned by its mother, so we took her in.
Our cat's mother didn't want her, so we took her.
ーMy cat was abandoned by its mother, so we took her in.
「うちの猫は母猫に捨てられて、うちで引き取った。」
My cat was abandoned by its mother. で「私の猫は(猫の)母親に捨てられました」と言えます。
be abandoned で「捨てられる」
ーOur cat's mother didn't want her, so we took her.
「うちの猫の母親はうちの猫をいらなかったので、私たちが引き取った。」
our cat's mother didn't want her「うちの猫の母親は彼女をいらなかった」のように表現することもできると思います。
ご参考まで！
カナダ 
