Java Framework for managing Tasks

I don't think that a there is a framework for managing tasks that could fulfill your requirements. You are on the right path using the Command pattern. You could take a look at the Akka framework for a simplified concurrency model. Akka is based on the Actor model:

The actor model is another very simple high level concurrency model: actors can’t respond to more than one message at a time (messages are queued into mailboxes) and can only communicate by sending messages, not sharing variables. As long as the messages are immutable data structures (which is always true in Erlang, but has to be a convention in languages without means of ensuring this property), everything is thread-safe, without need for any other mechanism. This is very similar to request cycle found in web development MVC frameworks. http://metaphysicaldeveloper.wordpress.com/2010/12/16/high-level-concurrency-with-jruby-and-akka-actors/

Akka is written in Scala but it exposes clean Java API.

I'd recommend you to examine possibility to use ant for this purpose. Although ant is known as a popular build tool it actually the XML controlled engine that runs various tasks. I think that its flag fork=true does exactly what you need: runs tasks concurrently. As any java application ant can be executed from other java application: just call its main method. In this case you can wrap your tasks using ant API, i.e. implement them as Ant tasks.

I have never try this approach but I believe it should work. I thought about it several years ago and suggested it to my management as a possible solution for problem similar to yours.

Eclipse's job scheduling module is able to handle interdependent tasks. Take a look at http://www.eclipse.org/articles/Article-Concurrency/jobs-api.html.