Can you lock the doors with the mechanical/emergency key only?
Are you sure you actually have an alarm fitted. On later Fiats, e.g. 500X then alarm was an option but if no alarm then an LED on the dash still flashes to indicated that the car is locked and the immobiliser is operating. Also a deterrent / alarm indication to thieves.
If you can lock with mechanical key only and the LED still flashes then you can check if you really have alarm by leaving a window open, locking the doors then reach through and open door from inside. Does an alarm sound?
I would have thought fitting an alarm to a motorhome would be odd unless you had a separate way of disengaging it. Motor homes are designed to be lock with residents still inside and moving about, sitting in front swivel seats etc.