Edna is the mother of Carl the Evil Cockroach Wizard and Brother Herman. She is a fire-breathing dragon while her sons are a cockroach and an ant. Edna's favorite son is obviously Herman; she always gives Herman compliments, respect, and love while she gives Carl the insults, the belittlement, and occasional love. Edna does know of Carl's desire for her love, and she has used it to get him to do things for her, as revealed in "An Inconvenient Tooth".
It's also revealed in Mission Yinpossible that, if she didn't overwhelm Herman in affection, she would do so with Carl. This signifies that, although she loves both of her sons (to an extent), she'll always pick one or the other as a favorite son. In the episode "Get Off My Back", it is shown that she prefers Yang over Carl (along with Herman). She briefly dated Master Yo while under a spell Carl put on her; however, in the episode "Yin Yang Carl", it is revealed that she still has a crush on him. Her (either dead, divorced or quest doing) husband, Carl and Herman's father, has not yet been shown in the series.