"Add content" button on related content node? Let's say I have 2 content types "Shopping center" and "Shop". 

"Shopping center" is a OG group.
"Shop" has node reference field "Shopping center". 

I would like to allow moderators to add shops to shopping centers on the shopping center node screen.

How to add "add shop" button on "Shopping center" node view ?
You are doing redundant work by having a node reference field. If "shop" is set up as a group post, you should be able to add new shops when in a shopping center context. There should be some kind of "group options" block that will give you these options. (Haven't done this exact thing in 7 yet but it must be similar to the way it works in 6).