Advice needed for self publishing cardboard children's book

I am planning to publish a children's book that I want to have printed on cardboard. My understanding is that it is basically impossible to print on demand for cardboard stock books (correct me if I am wrong). Does anyone have any recommended printing services? When you self publish in bulk, what are options for third party storage and shipping when copies are sold? Basically I need a self publish for dummies guide if anyone knows of one.

Thanks in advance!