A person who is overly emotional. They disturb the peace in a group of friends by always being angry, crying, laughing hysterically at things that are only worth a chuckle and telling everyone his or her problems. This person is likely bi-polar. A single best synonym for drama mama would be "angsty one." The word angst means an intense feeling of emotional strife. A drama mama fits this profile.
The mother of any child whose sole purpose in life is to become a famous actor/actress in film, tv, or theater. Often, the child is already in a performing arts program at school or through outside classes such as acting, dancing, voice, etc. These mothers have drama 24/7.
I don't want to hear your complaining about not getting the part you wanted; go tell it to your dramamama!