You do not need accreditation from Yoga Alliance to teach kids yoga professionally. It's neither essential nor expected by parents or schools.
To teach kids yoga, make sure you’ve been well trained, and that you have professional liability insurance and (in some markets) a background check to work with kids (DBS in the UK). This is what schools and parents expect. It protects you too.
We developed our training with the support and insight of an insurance company in the UK - DSC Strand. The video appraisal process and the criteria for certification were agreed with them. They still underwrite our course - and there is a long list of insurers around the world who cover graduates.
For what it's worth, Jaime is an RCYT (Registered Children's Yoga Teacher) with Yoga Alliance. She qualified before 2010, when Yoga Alliance started to stipulate that all RCYTs had to do a 95-hour face-to-face course with a Registered Children's Yoga School.
She is also an E-RYT (Experienced Kids Yoga Teacher) with Yoga Alliance. This means she's a registered adult yoga teacher (RYT-200) who has taught yoga for a certain number of hours. We decided to pay the extra for Jaime to be recognised as an E-RYT because it was a requirement for any leader of a Registered Children's Yoga School (RCYS). In the end we decided we didn't want Cosmic Kids to become a RCYS because we are an online school and Yoga Alliance don't recognise online training - or at least they only recognise it for Continuing Education hours for qualified adult yoga teachers rather than their full certification as an RCYT.
In the end, we decided to get on with making the best training we can and making it available affordably and online. We now have more than a thousand graduates out in the world teaching brilliant kids yoga professionally.