A physician sedating a child, especially a mentally disabled child, for a short, minimally painful procedure wouldn't be very likely to use Ketamine. Ketamine doesn't relieve anxiety all that well, which is what the mother is worried about in this case. It takes about three hours to wear off and once it does start to wear off it has been known to cause psychological issues such as agitation, confusion and hallucinations which would be something to be avoided at all costs when dealing with a mentally handicapped child who had just undergone a potentially traumatic experience. The drug most commonly used to sedate people and alleviate anxiety caused by invasive procedures is Midazolam (Versed), a short-acting benzodiazepine that wears off in less than an hour when administered intravenously. It is far less likely cause any adverse psychological issues and it has the added benefit of causing memory loss, most people don't remember anything that happens to them while under the influence of Midazolam which is another benefit when dealing with children.
Barba risks his job and his license to practice law by intentionally causing a mistrial and then asking the judge to move the case to family court, thereby allowing Mariel to be sentenced as a minor because he felt that she didn't deserve the prospect of spending the next 25 years in prison for being convicted as an adult for second degree murder. However he didn't need to take this tremendous risk, as an ADA he had the authority to offer Mariel a plea bargain considering the extenuating circumstances of the case. Mariel was obviously under extreme emotional distress after the years of abuse she suffered at her mothers hands, so it would of been perfectly reasonable for Barba to plead her down to manslaughter in the first degree and recommend she be sentenced as a minor, meaning she would only have to spend three years in a juvenile facility.