Check that you are a member of the family group. Settings > [Your Name] > Family Sharing. A list of members will appear at the next screen including your Apple ID if all is well.
Have you accepted your relative's invitation to join her group? Did you get confirmation that you were admitted?
What tells you that you are backing up outside the family group? If you go into Settings > [Your Name] > iCloud you will see the plan to which you are backing up, and one of the categories of data use is Family. You will see something like: Photos, Backups, Others, Family. Clearly if you are part of the family group this will be present.
Is your Apple ID present in similar lists on your relative's device(s)?