It also depends on available money. Any work involving machinery, e.g. digging up earth/concrete is going to be costly.
Another option, depending on the ages of the children, is to level the concrete using some sort of exterior leveling compound, incorporating a "fall" or slope to deal with the rainwater. Possibly going to a covered gully between it and the garden.
Then install astroturf/artificial grass, a sandpit and play-area for the kids, all on the newly leveled/astroturfed concrete section.