Can I use multisite for parentdomainA.com, childdomainA.com and childdomaiB.com?

@jzee,

Setting up the domains that way is certainly possible. You will need to use this plugin:

http://wordpress.org/plugins/wordpress-mu-domain-mapping/

Also, this book is really helpful and is PWYW (pay what you want):

https://store.halfelf.org/ebooks/wordpress-multisite-101/

The parent should act as a database and website that shows all products, the children should each get their specific products from the parent and display just the products specific for their domain.

There is no ‘built in’ capability to do what you are talking about, but it may be possible with some clever use of categories and/or tags.