If you're not 100% sure its petty spurge, add a photo to your question. If it is petty spurge and its widespread (which it sounds like it is) then this is going to be an ongoing project, because each plant, if left to go to seed, produces hundreds of seeds which will all be in your soil and waiting to germinate as soon as they get the opportunity.
If the soil is damp, they are easy to pull up by hand because they don't have a deep root system, though gloves should be worn to do this. This is the most ecologically friendly way to deal with the problem, but obviously requires physical effort. By now, the plants you have growing will already have dispersed their seed, unfortunately, so vigilance is required from early next spring onwards to uproot any plants that start growing. Regular hoeing should help keep them down.
If its growing in the cracks of the patio, you can scrape them out with a patio tool, and/or, in spring next year, apply Pathclear, which will prevent weed growth for up to 3 months. Make sure your child is excluded from the area until the solution has dried - Pathclear is systemically worse to be in contact with than the spurge sap. You might want to reconsider re-pointing the patio, or replacing it so there are no gaps for weeds to grow in.
Further info here https://www.wyevalegardencentres.co.uk/tips-and-advice_how-to-control-petty-spurge