In my view, It is better that you use AJAX instead of using Applets.
Applets are very lazy and heavy loading components although before
AJAX they are the only dynamic components in Java Web World!

How are your applets  connected to the database? Is it through a JEE layer? If so, I don't think JEE is the best choice for push architectures unless you wanna do crazy things. The best is to define what your real  time quantum is and check the server periodically.

I don't know if there is a framework  for your requirements, But I think observer design  pattern could help you. The model you are talking about is an implementation of observer pattern.

you can use "call back" pattern..............

If you are forced to use java components (i.e. AJAX rejected), use JMS for the former case and use synchronization like what Farzad said for the latter.
Strictly speaking, your first applet  should subscribe to a JMS topic and get informed whenever changes occur, and your second applet checks periodically and does necessary synchronizations.