Hi finding,
Welcome! Sorry about your situation and your children.. Must be really difficult for all of you. I never had kids so I couldn't even begin to imagine how difficult it must be..
In any case, have you read Dr. Jernigan's book "Beating Lyme Disease?".. It not, it's a great book filled with lots of information. I would start with that. Since his botanicals are all natural, I believe children can take them but to be sure I would first have a telephone consult with Dr. Jernigan and explain your situation to him. I know he has treated many children with success.
His book can be bought at this site:
http://www.hansacenter.com/books.php
You can read about the treatments here:
www.hansacenter.com
Hope that helps,
Denise