First make two copies of the mIRC shortcut where you want them. You need to use these two shortcuts to start the two different mIRC sessions. Then right-click on the first shortcut, and click "Properties". Your Target field should look something like this:
"C:\Program Files (x86)\mIRC\mirc.exe"
It may look slightly different depending on what version of Windows you are using. Anyway, add the following on to the END of the target line without deleting what is already there:
So, in other words, the entire line will now look like this:
"C:\Program Files (x86)\mIRC\mirc.exe" -r"%appdata%\mIRC"
Hit OK. Now do the same process for the second shortcut, but use the following text instead:
Thus giving you something like this as the whole line:
"C:\Program Files (x86)\mIRC\mirc.exe" -r"%appdata%\mIRCbot"
That's it. You should now have two completely independent sessions of mIRC that won't interfere at all.