Posted: 14/04/2014 at 11:27
If it was me (and I'm well aware I'm not you and I only know part of the story here) I'd have a go at renovating that lawn. I've dealt with far worse and got -a decent play-lawn out of it.
My guess is that when you turfed it you used the lawn far too soon so it became uneven - you have to keep off freshly laid turf for quite a while, and after than, only gentle walking, not heavy duty play! It has also not been mowed regularly enough. Lawns need mowing at least once a week, sometimes more, right through the growing season.
I would kill off or dig out the bigger weeds (I've zoomed in - there aren't that many) and mow the lawn with a rotary mower set on high. Treat with an all in one Weed & Feed and keep mowing - the grass will begin to grow outwards rather than upwards - then you can fill in any hollows with topsoil and seed over them - you'll soon have a lovely green lawn. It will never be a bowling green, but you have children - you don't want a bowling green. Soon you will be able to lower the mower blade, but never cut it very low - it will scalp the grass and weaken it. Little and often is the way to get a good lawn.
Even if you take all that grass up and turf it now, your new lawn will not be able to withstand children playing on it 24/7 (or even 12/7) for the first season.
If you do what I suggest they can play on the lawn all this summer - just ask them to be careful of the re-seeded bits - they can even have little watering cans and water them for you when the sun is shining.