The preferred donors for kidney transplants in young children are adults, not other children. Kidneys from pediatric donors can have more technical complications, simply because the blood vessels are smaller and more likely to clot. Also, kidney function doesn't mature to adult levels in the first two years of life, so the function of a kidney from a young child may not work as well in a transplant setting. Pediatric kidneys from deceased donors are used for transplantation, but they're typically transplanted as a pair to an adult, rather than individually to another child.
The idea of using kidneys from children for transplants in other children sounds like common sense, and it was a standard practice in the 1980s, but the complications were quickly discovered and adult kidneys became the preferred donated organs. This change in practice was followed by a change in UNOS policy, which resulted in significantly better outcomes for young children with kidney transplants. While there have been a few instances of people under age 18 being living kidney donors, the youngest has been a 7 year old identical twin, and there's no indication that any of these donors were sought for size reasons. Finally, 46 children under the age of 5 received a kidney transplant from a parent in 2010 (source: OPTN Data Reports) so the Riveras' idea that they could be kidney donors for their child is backed by a mainstream practice.
Maybe I shouldn't be surprised that the ideas being spread about pediatric kidney transplants are 20 years out of date, since the contraindication of "mental retardation" should be equally out of date. But I do wish the coverage of pediatric kidney transplants was better than the news that's out there. By "better" I mean that hundreds/thousands of parents have donated kidneys to their children, that pediatric kidney transplants are done in a huge variety of circumstances, and that most people working in the field are dedicated to all of their patients and show it every day.