As far as I know interviews are conducted individually?
Also, I was under impression your mother can still attend the interview as scheduled and send medical exams in later as required. That way nothing needs rescheduling. But then, once both parents get their visas they can enter the US together.
Some things are just out of your control. For example, even if you reschedule interviews, one parent may take longer to get approved than the other. I see no benefit of rescheduling interview to be on same day, just like I mentioned earlier I think they'd be interviewed separately anyways.
Others can correct me.