Go to headlice,org.
One thing I did when we had kids that were infested and sharing it in the classroom was to make a tea tree spritz bottle.
Go buy some Tea Tree Oil from the Ethnic Hair section at Walmart. I bought a small, 8 ounce or less, spray bottle from Walmart too. I filled it with filtered water from the fridge, we have hard water, and then I added several drops of Tea Tree Oil, maybe even a half teaspoon. Put a few drops in every bottle of shampoo you own too and it will be "in" the hair shaft even deeper.
Each morning when you go to fix their hair for school shake the spritz bottle up very well. Then when you spray their hair to dampen it to brush it and style it you are putting on a layer of protection against head lice. It's also good for people so it can't hurt.
You are poisoning your family. Don't let them come over anymore unless you sit down with the mom and grandma and let them know what you're going through.
Their car could be re-infesting them, their dining room table, they may not be getting all the live bugs out, the white nits don't mean anything. They are empty egg shells. They come out easily if you simply wash the kids hair then condition it very well. Rinse it then leave it drippy wet. The water stuns the bugs, they breathe air just like we do and the water and cold from the hair being wet slow them way down.
Go through that child's hair in about 1 inch sections, root to end. Use a magnifying glass so powerful you can almost count the hairs on their heads.
Have a cup of water next to you. Any living bugs get pinched out with either tweezers or your fingernails and into the cup of water. They drown. Then if you see any egg shells or eggs with a black center, an unborn baby, they slide down the hair shaft when you use your fingernails. If you don't have nails you can use a tiny pair of scissors and clip that single hair. You don't want to make the child bald, it's better to slide them off.
I have dealt with lice a few times. I have used a lice shampoo one time. I never had any time when I couldn't have them gone in a couple of days and I NEVER tore up my house or did anything drastic like some of the people on here do. It's not necessary. Vacuuming takes care of 99% of them. Washing sheets and pillow cases and couches and carpet and car seats and carpet should take care of any living bugs.
The bugs are slow and do not jump. They can fall on another person if they're playing, say...like on monkey bars. One kid is hanging upside down swinging and another child is below them.
It's hard to share lice. Using each other's brushes, wearing each others winter hats or coats or scarves, dress up clothes in a classroom or play area, laying side by side with their hair touching for extended periods of time so the bug can crawl for one head to the other.....
Clean all the hair brushes and combs in hot soapy water, let them soak a bit. Spritz them with the tea tree spray bottle of water.
One thing you can also do is report this to their school. Tell the school that you've had the kids over a few times and you've looked in their hair and found bugs and seen nits. Tell them the evidence, proof they have it.
Just "I get lice every time they come over" isn't proof of anything except that you have lice. Lice could be coming from your house to them actually. Your house could be reinfesting them if you're not getting rid of them. Lice shampoo doesn't do much of anything.