A play area will always ruin your lawn, you may be wasting your time redoing it.Plan your garden so you can enjoy your grandchildren playing and still look at a nice lawn.
Is your garden in the shade(Large trees etc. ) as this will stop your lawn developing.
I suggest if you are going to go ahead with renewing it then wait until April and treat the existing and remaining grass with weed and feed -gets rid of any moss and weeds , then sow a hard wearing grade of grass seed( you can get this at any garden centre),about 10 days later but you will have to stop anyone using the area.will take about 2 weeks to show and will need to be a whole season to establish.
Is it possible to keep the play area separate and put down a rubber matting ground cover and rope off the lawn to protect it.