Diaper bags are not usually considered as carry on luggage but you're still allowed to carry the diaper bag onto the plane because you'll need the diaper bag to change diapers and feed your baby.
Diaper bags just like purses and laptop bags are considered to be personal items and do not usually count towards your carry on.
So you can bring those extra diaper bag and other personal items such as your purse onto the plane along with your other carry on luggage.
So you can have your regular carry on luggage onto the plane along with a purse and diaper bag if you need too.