I don't know about the summary in the youtube link you posted but after reading several articles on the case, I didn't find any of the allegations you mentioned in your post (claims that she was a convicted domestic abuser, on probation at the time of the shooting & specifically shot at the children).
I'm curious…. is your information found ONLY in the youtube link?
Marissa Alexander Gets 20 Years For Firing Warning Shot (VIDEO)
TAMPA, Fla. -- Marissa Alexander had never been arrested before she fired a bullet at a wall one day in 2010 to scare off her husband when she felt he was threatening her. Nobody got hurt, but this month a northeast Florida judge was bound by state law to sentence her to 20 years in prison.
Alexander, a 31-year-old mother of a toddler and 11-year-old twins, knew it was coming. She had claimed self-defense, tried to invoke Florida's "stand your ground" law and rejected plea deals that could have gotten her a much shorter sentence. A jury found her guilty as charged: aggravated assault with a deadly weapon. Because she fired a gun while committing a felony, Florida's mandatory-minimum gun law dictated the 20-year sentence.
Her case in Jacksonville has drawn a fresh round of criticism aimed at mandatory-minimum sentencing laws. The local NAACP chapter and the district's African-American congresswoman say blacks more often are incarcerated for long periods because of overzealous prosecutors and judges bound by the wrong-headed statute. Alexander is black.
It also has added fuel to the controversy over Florida's "stand your ground" law, which the judge would not allow Alexander to invoke. State Attorney Angela Corey, who also is overseeing the prosecution of shooter George Zimmerman in the Trayvon Martin case, stands by the handling of Alexander's case. Corey says she believes Alexander aimed the gun at the man and his two sons, and the bullet she fired could have ricocheted and hit any of them.
At the May 11 sentencing, Alexander's relatives begged Circuit Judge James Daniel for leniency but he said the decision was "out of my hands."
"The Legislature has not given me the discretion to do what the family and many others have asked me to do," he said.
The state's "10-20-life" law was implemented in 1999 and credited with helping to lower the violent crime rate.
Anyone who shows a gun in the commission of certain felonies gets an automatic 10 years in prison. Fire the gun, and it's an automatic 20 years. Shoot and wound someone, and it's 25 years to life.
Critics say Alexander's case underscores the unfair sentences that can result when laws strip judges of discretion. About two-thirds of the states have mandatory-minimum sentencing laws, mostly for drug crimes, according to a website for the Families Against Mandatory Minimums advocacy group.
"We're not saying she's not guilty of a crime, we're not saying that she doesn't deserve some sort of sanction by the court," said Greg Newburn, Florida director for the group. Rather, he said, the judge should have the authority to decide an appropriate sanction after hearing all the unique circumstances of the case.