Scott,
Depends at the end of the day but the Best Practice here would probably be to use the shortcut option and make the projects of the specialized team(s) as a shortcut within your Project (i.e. within "bigger project").
If a shortcut does not do it, the other option is to create Tasks for those teams that need to be completed. You can even create customization workflows that once Project A is updated, update project B. This would be more complicated and would probably require hours with a Customer Success Manager or Professional Services to provide a solution.
Sincerely,
Boris