Your HMO's applet is either far too large or their server was being very slow and very difficult.
I have had multiple slow experiences with different applets and different machines. If developers bust their balls, then yes one can make a smaller applet (usually by moving as much of the biz logic to the server as possible. Which brings up another issue: biz logic on the client is relatively easy to reverse engineer. Bytecode labelers and analyzers readily exist.)
It is moot anyhow, because MS is pulling the plug on most Java in their browsers, making it even less consistent than before.
The Java Applet model is pretty much dead.