What a wonderful question! My opinion is that following medical model of mental health services, that right has been taken away already; however, other models of services could retain that right.
Similar problem is occurring in understanding of harm done to victims of wrongdoing. From the legal perspective, harm is measured objectively (injuries and money); from the psychological perspective, harm is a subjective perception and should be measured as such. I would hypothesise that Happiness is also dependant on cultural scripts.
this question is contextual and could be related to culture and several other factors that relates to the free will of the individual. Though individuals may have the right to define his or her own happiness using the free-will bases, this might also be harmful to others or the individual where the effect or envisaged outcome might bring negative outcomes. So due to several factors this right might be contained or managed when exposed to other intervening factors.
I agree with Adeleke on considering individual differences between definitions, individuals also comply to their reference groups (work groups or larger cultures). A system could be viewed as the culture with inclusion of formal (written rules). When the system places priority on written definitions of happiness, then, individual rights to make own choices are limited.
"To be happy is to love, to be happy, then, is to suffer, but suffering makes one unhappy, therefore, to be unhappy one must love, or love to suffer, or suffer from too much happiness — I hope you're getting this down." — Woody Allen
What does "defining" happiness mean? Happiness is a psychological state of a human being that may be caused by different things for different people. Just because different things make us happy it doesn't follow that our definition of the term "happiness" is different. Compare: just because we may have different favorite beverages for quenching our thirst it doesn't follow that we have different definitions of "quenching thirst". Talk of "having a right to define happiness" is a misleading way of talking about having a right to pursue the things that make us happy, which is not a matter of definition. If we all had different definitions for the term we'd be talking at cross purposes when we use it in conversation.