Actually, the school will check her head for nits before they will let her return. The parent could bring in an empty bottle that they did not use on that child.
Are there other lack of care concerns for your step-daughter's welfare? Is she safe and healthy except for the lice? Is the house reasonably clean, free of spoiled food and rotten garbage. Are there mice? How about animal feces on the floor. Does your step-daughter get enough to eat? Is she adequately supervised? Has she had her immunizations? If not, you may be able to get them involved after you list and document several concerns.
You might also be able to have a public health nurse make a home visit and offer to help the mother stop the cycle.
As to not affording a lawyer, you can get one from Legal Aid on a sliding fee scale. Or you can talk with one who specializes in child custody issues to ask for advice. Usually the first visit is free. You only start paying once the attorney and you determine that he can help you.
And do not bring up the issue of custody when talking with CPS, public health, or any other government agency when asking for help. It is too easy for them to assume that you are trying to use them to get custody and they do not want to be involved in a custody battle.
I'd suggest that you make taking a bath along with washing her hair a no big deal routine when she comes to your house. I've not heard about the tea tree oil but if that works it's ideal. Then use a nit comb and make a game of getting rid of the nits. Put all of her things that are washable in the washer. Make it a fun game. My 6 yo granddaughter is very aware of "things" that make people sick and would love that game. Also I think lice make the head itchy and she would like to get rid of the itch.
You could have a separate set of clothes and toys at your house that are also part of the routine of coming to your house. My granddaughter has toys here and often doesn't even bring over any from her house. And I keep clothes for her here. Those clothes do go back and forth but they wouldn't have to. She comes over nearly every Friday after school and frequently asks to have a bath. She loves water.
I know that doesn't deal with the problem of getting the mother to take responsibility. But it will help you to keep the lice out of your house.
I may be way off base here but has your husband talked with his ex about the lice and what can be done and offered his help? Compassionate conversation often leads to problem solving. To work, one has to have patience and a real concern for the other person's difficulties. It may take several conversations especially if there has been fights prior to this.
I hope this helps and I hope that you can find a way to get rid of the lice. M.