The question of whether she was acting in a "sudden passion" or whether there were other mitigating factors only applies to the penalty portion of the case, AFTER she's been found guilty of murder. We don't have second degree murder in Texas. It's murder or capital murder, and capital murder doesn't apply here.
The defense attorney is deliberately trying to blur that distinction so that the jury will find that she's not guilty of murder, and the judge should not let him get away with it.