There isn't a way to change the order of Guardians shown in the Family, Guardians and Contacts section of the student profile.
If guardians are all the same priority, it will order them based on the profile that was added most recently. Whether the guardian is Primary, Legal, Authorised to Collect or Student Lives with Guardian does not have an effect on the order shown.
How to change Guardian Priority
There is no way to change the guardian display order if they have the same priority, but you can change the priority for each guardian.
Click on the guardian you wish to change the priority for in the Family, Guardians and Contacts section, and click Edit.
Change the priority from the Emergency Contact dropdown, and click the green Save Changes button.
Changing the order of the Emergency Contacts on the right-hand side of the student profile
There isn't a way to change this order if they are the same priority. This order comes from the priority and when the profile was added.
If a Guardian in the Family, Guardians and Contacts section isn't appearing in the Emergency Contacts section, they will be down as 'Not an Emergency Contact'.