I have done something similar before, and this is the way I approached it.
In your "parent" project, create an issue for each "child" project.
Then, convert each issue to a project, leaving the issue in the "parent" project. This will build the link between your parent project and the child projects.
When a task is updated in the parent project, now you can pull in the resolving child projects, find the paired task in those child projects, and update those tasks.