A double room means a room for two people. Whether it has one or two beds is something that, if it is not stated in the hotel's brochure/Web page, you have to ask directly. Most hotels have more two-bed rooms than one-big-bed rooms in my experience, because they are more flexible.
An additional bed is called in Spanish 'cama supletoria'. It is uncommon to request for two 'camas supletorias', but some hotels can have rooms large enough to fit them. I've never asked for it, so I can't provide first hand experience. When contacting the hotel, I would say clearly that the beds are for two kids, and not for four adults sharing the room (they can suggest you to book two doubles instead). Some hotels have communicated rooms (with double door) that can be another option to consider.
Another Spanish words that can be of use in your search are 'Habitacion triple' (room for three people), and 'Habitacion cuadruple' (room for four people).