Q.How to kill purslane
I have read a lot about Purslane and am very familiar with it in my lavender. In the past, I’ve always removed it by carefully pulling it out of the ground including the root and immediately put it in a plastic bag. Is there a post-emergent that I can use to spray on the root if it breaks off and remains in the ground? I’m also aware that each plant has hundreds of tiny seeds, which I try to contain. Should I spray a pre-emergent to kill the seeds in the spring? What is your best recommendation for getting rid of Purslane?

Here is an article that will help you.
https://www.gardeningknowhow.com/plant-problems/weeds/purslane-control.htm