It seems like you need to position this service very carefully, since there is likely not a bright line between some of the issues parents might come to you for, versus seeing a pediatrician, behavioral health provider, or other health care provider.
And indeed, traditionally that's where parents would go with some of these issues (sleep issues, tantrums, etc.).
But your FAQs emphasize that you're not a health care service -- yet I wouldn't be surprised if parents rely on you to at least bring up when a health care provider should be brought into the loop.
Just out of curiosity, what would you say this service is intended to replace? Are your prospective subscribers people who would otherwise be reading books, poring through Internet advice, consulting friends and pediatricians, etc., and this service just saves them time versus the DIY alternative? Or are you courting people who have no idea how to do that stuff and their alternative is just suffering through it as best they can?