I don't think so, Ursa wasn't a good mother, even to Zuko. She could have just took Zuko to her to live with Ikem and Kiyi, also Ursa could take Azula with her, if Azula resist or will do something impulsive, Ursa could lull her to sleep with something without Azula knowing that and without Ozai discovering nothing. Also, instead of being cruel (unintentionally) to Azula, she could be very patient and emphatic to her instead of just Zuko and Kiyi, why Ursa had Azula if she won't take care of her just like Zuko? She is also Azula's mother.
She could do that, but she didn't.