Many valid points have already been made in this thread saying why we cannot help people on how to hide mIRC completely.
Hiding mIRC is not going to prevent your dad from knowing it has been installed. It must still appear in Add/Remove programs and he's bound to look there some day.
You can always use /showmirc -t to minimise mIRC to the tray.
As has been mentioned somewhere else before though, we respect parents decisions just like we respect the decisions made by schools, universities, work places etc about firewalls/routers and restricted IRC access. If your dad doesn't want you to install programs on his computer then he has that right. And if he has important files on it that he cannot risk getting deleted by some virus (whether it is contracted accidentally or not) I must say I can see his reasoning.