I've been working on this all day. Yesterday, I installed the update (from the Java website, not through the updater in control panel) on two computers and homegroup stopped working. I did a system restore on both computers and homegroup started working. Then I updated Java again and homegroup stopped working.
I'm not sure though because I did some other things, but the one constant was that after the Java update each of my homegroup computers couldn't see the other. Leaving the homegroup left both of my computers still not seeing the new homegroup was then newly created. In other words I never got the "join" button.
If you installed this update and your homegroup stops working, please let me know. The homegroup troubleshooter is not able to resolve the problem. The network is still fine -- in other words "WORKGROUP" is happy and continues to share just fine.
The only way I could get my homegroup back was to do a system restore. I can do just about anything else, including using CCLeaner to clean the registry, but I only appear lose the homegroup when I install the Java update.
Still, I could be wrong. I'd like confirmation one way or another. This is 32 bit Java and I use Firefox if it makes any difference.
Make a restore point before testing. I'm done with it for now and I am not installing the update until it is known to be safe.