This will be best done by using dependencies. Since you already have the groups defined, it will be pretty easy to do this. Just create a dependency, and make a parent and child. Either can be a group. When a parent is down, the child group will go into 'unreachable' instead of down. And you won't get all the extra alerts.
Thank you for the quick answer. I just printed out the information on setting up the dependencies. I will give that a try.