If head lice threatened custody of any sort, no one would have custody of their children. The best way to get rid of them is to actually pick nits out of the hair. Combs are not 100% effective. This takes several sessions and life cycles of lice to get rid of them, as nits are easily missed.
Go through her hair a very small section at a time. I would suggest putting on a favorite movie of hers so that she would have patience to endure this time-consuming procedure. Put any nits that you find into a glass of vinegar and flush it when you are done.
Lice are becoming more resistant to chemical treatments. I wouldn't recommend putting any more pesticide on her head to treat them.
This is the advice given by our school nurse, and I was a school nurse too. Lice just aren't that big a deal, except to ex-spouses. Kids share them all the time. I used to send DS to school with a plastic grocery bag. This was to be used for his coat. Hanging coats next to each other is a great way to get lice, too.
Good luck. Getting rid of lice is not easy. Sharing households makes it harder. She's probably getting them over there and mom checks when she returns from your home. Then she doesn't check before sending her back. Your ex is also a nurse, I remember. So of course, she knows more than you and the CDC....
Or I could be full of hot air about relationships. Wouldn't be the first time. You had the loser for a judge, I remember. So you might want to document all the things that you have done to treat them....have her prove what she has done to treat the lice. Save receipts, rent steam cleaners, etc....