I've still not found sources about "private child chains" and I doubt it will be possible to create totally private chains (with not even read access for the general public) inside the Ardor platform. Afaik the private chains are the forks of Nxt/Ardor for businesses. Possibly, creating child chains could remain a paid Jelurida service for a longer time that I expected initially.
I will decide my final position on Ardor when this point becomes clearer - if control is too centralized and license terms too restrictive, then I'll not longer supporting it.
Chain can be "private" only if it tokens are not in free market, I mean you cannot use chain, if you don't own its tokens. But technically it will be public in Ardor platform, also bundlers of this chain has to pay ARDR in odrer chain transactions to be included in the main chain.
And yes, it was said many times publicly by devs, that at the beginning, creating child chains will be manual, by devs and it will be paid service. Ability to create child chain without devs is planned for late 2018 or 2019. Of course there will be a fee for this, but this fee will go to ARDR forgers.
And here is a proposal of new JPL license by Jelurida: https://www.jelurida.com/jelurida-public-license
EDIT: P.S. but this discussion must go to https://bitcointalksearch.org/topic/ardor-scalable-blockchain-as-a-service-platform-proof-of-stake-1518497, as it is Ardor related