You should never use the word parasite or worm. People do not believe this, not even close relatives. I would tell them cancer or something similar. Tell them you are terminally ill. Tell them you have thought parasites but doctors just found out it is cancer. You need help. Get help. After you are clean, you can tell them, or not. Does not matter, your goal is reached. No need to convince anyone of your truth. Just get help.
Yes i am sure you are worried about your kids. I am worried about mine too. But you need to get well to help your kids. As long as they are ok, their immune system will cope. You can treat them after you are fine again. Dont kiss them on lips and clean the toilet with hydrogen peroxide, the toilet seat too. Dont share food, drink or cutlery. Trust me it will be fine.