Was what the wife did correct, regarding partially bathing and making up the days of menstruation after being discharged from the hospital, or is there something else she should do?

If a wife is unable to use water for ghusl (definition) after purification from menstruation due to the unavailability of a suitable place, she should perform tayammum (definition) and pray, and there is no make-up (qada') for her. However, if she prays without performing ghusl or tayammum, she must make up the missed prayers. If she fasts after purification without performing ghusl, her fast is valid because purity is not a condition for the validity of fasting. She is only required to make up the days she missed due to menstruation.