First thing first, there is no immigration desk when u traveling from Ireland to UK due to common travel area.
Next, in any case if there is immigration officer (just for argument sake) she can enter to UK without any issue as ur wife left UK in a good time before the expiry of her first pemission.
Next, if you want to avoid any hessel (Again just for argument sake) you can travel to UK and Ireland (back and forth) via belfast, (if you use George best city airport) you will not see any immigration officer at all.
LOL, I am giving you MILLION dollar advise
Good Luck