"My children are not royal; they just happen to have the Queen for their aunt"

This quote by Princess Margaret speaks with the idea that her children are not privileged or entitled simply since they are related to the Queen. She is highlighting that her kids are not of royal blood, which their familial connection to the Queen does not provide any special status or advantages. Princess Margaret is most likely making this indicate highlight that her kids are not any different from other kids, which they should not be dealt with as such. She is likewise most likely trying to secure her kids from any possible criticism or judgement that may originate from their connection to the Queen. Princess Margaret is emphasizing that her kids are just like any other children, and that they need to be dealt with as such.