Too late for seed in the UK, I'm afraid, although down south or in the west country you might have got away with it. You can seed in late March/early April, but, it looks like you've got children; grass seedlings cannot be walked on normally for 3 months, and certainly won't survive children's feet or normal play during that time, which would mean your roping off the area and keeping everyone and everything off it till the end of June. And that, I suspect, will be highly inconvenient, but if you decide to seed, use play lawn or any seed with short leaved rye grass in the mix.
October is, though, the best month for laying turf in the UK, provided the ground is not waterlogged, so you might want to consider that instead, because that can be used more or less normally after 4 to 6 weeks. Whether you want to seed or returf, preparation is required, and that involves digging it over, removing any weed roots, levelling, walking over it closely on your heels to get out soft spots, raking it over, relevelling, then raking up the top inch to give a fine tilth, and then either seeding or turfing. Regarding the area where you spilled glyphosate, if that was within the last week or so, wait another 2 weeks to prepare the area.