My house has Exterior & Interior insulation. Would it be advisable to remove the internal?
It sounds like you are willing to spend money to remove something that that is designed to help save money. If your houses walls are made entirely of brick and mortar the two layers of (rigid) insulation is the only material slowing the heat from conducting through the walls. I think you will find most, if not all, information and scientific data states the more (thicker) insulation in a conditioned space the less energy will be loss from heat conductance. If I can suggest that a better question posed here might be how to hang a shelf on a insulated brick wall. It could save you an un-needed financial burden.