When I try to set the shape of an existing node, my code works fine with IE9
With Firefox, Opera and Chrome I always get this error:
Uncaught exception: Error: java.lang.IllegalArgumentException: No method found matching name setShape and arguments [sun.plugin2.main.client.MessagePassingJSObject]

my code:

var selectednodes = diagram.getSelection().getNodes();
var node = selectednodes.get(0);
var shape = scriptHelperShapes.shapeFromId("Decision");
node.setShape(shape);

node does exist. When I try:
    var test = node.getText();
test has the correct string.

Thanks for this suggestion, it works great now.

I cannot use applet1.getnodes().get(0).getShape()
in applet2

But I can use this shape:
applet2.scriptHelper.shapeFromId( applet1.getnodes().get(0).getShape().getId() )

Technically you are still passing a Java object (of type String) from one applet instance to another. This is a confirmed bug in the Java plugin, which our developers reported to Sun/Oracle some time ago; you could vote for it here:
http://bugs.sun.com/bugdatabase/view_bug.do?bug_id=6989193

As a work-around you might try first converting the Java's string to a JavaScript string by calling the String's constructor:
var jsStringId = new String(applet2...getId());
applet1...(jsStringId);

Obviously this will not help for passing other types of Java objects between two applets, so you'd better use a single instance of the DiagramApplet class. That bug is one of the reasons we moved the misc. controls to the main DiagramView applet in this release:
http://mindfusion.eu/Forum/YaBB.pl?num=1331713838

If you absolutely must show two DiagramViews on the page, we'll think of some way to support this from the same applet.

I hope that helps,
Stoyan