by the way, many hotels say no more than 2 people but they mean adults or older kids
I would check with the hotel but many will allow 2 adults with 2 young kids using existing bedding
the difficult part is finding a hotel with 2 double beds vs one larger bed or 2 twins.
I assume that you will not leave the two kids alone in a room unless they are adjoining rooms.
why not just bring 2 very thin sleeping bags and let them "camp" on the floor while you are on vacation.