You are missing the point
Its like an old "joke" I have heard:
"Do you know that 60% of the accidents happends at home??
... Don't live at home!"
Yeah, that would solve the problem, but being more carefull at your own house would be more practical then living at someones else house.
This is the same thing here.
I'm not so sure that working with mozilla will solve the problme either, cause the problem happens because mIRC open a connection to members.lycos.co.uk, and then IE sends data, the server of lycos sees that the same IP sends data (it doesn't know which browser sends the data), but then it causes the an error, cause both browsers are connected to the same server at the same time.
My question is how can it be solved??