For car, you need to consider installment, road tax, insurance, petrol, ERP & parking charges. If you get a car you'll also need to get car seat(s) for the children.
I think it would be reasonable to say that you have to set aside at least $1k a month for the car installment, petrol, ERP & parking charges. Insurance depends largely on the driver's experience & whether you guys are paying for it by installment or 1 off.
But do note that it depends a lot on the driving pattern of the family. For my family, besides our weekly visits to our parents' place, my hubby also uses the car for work purposes, thus we feel it's worthwhile to get a car.
I think as much as household income is important, it also depends on what your family's expenditure is like. Some families find the car a more convenient option than public transport, so they may sacrifice other types of spending to accommodate financing the car.