As mentioned elsewhere in the forum, never open two connections to the same network. 1) It messes up settings. 2) It messes up how things work.
If you want to use another nick on the same network, you'll need to open two copies of mIRC/Invision. Note that to prevent settings errors in Invision, you should not just open the same copy of mIRC/Invision twice. Install it to two different locations and then open both copies.