it depends where. In the US, occupancy by 4 people (doesn't matter adults or children) is pretty standard in pretty much most hotels as it's very common to have 2 queen beds as a bedding option. In Europe, i would say it's almost impossible to get a room with 2 queen beds as the rooms tend to be smaller with space for only one bed - thus no way to fit in 4 people to sleep.
Asia is also usually pretty generous on 4 occupancy except Japan.
So, where are you trying to book? Also, look at the actual room choice - is there actual space for 4 of you to sleep? Would the 2yo sleep in the a crib/travel cot? If so, you can skip him in the booking (a little iffy, but should be ok) and request a crib/cot.
For each room, when you click on room details, it will show you max occupancy.