Please communicate to the guest that the following will happen: Since she has requested and paid for only 4 guests, if 6 guests arrive at the location for check-in they will be denied access and they will forfeit their entire rental due to a violation of the house rules regarding accomodation. This means the guest will be out for the entire amount of the reservation, not just the extra $22/night for the 2 children. Then send her a modified reservation request for the additional guests to encourage her to book the room correctly.
Of course, there is a very diplomatic way of saying this which I have not done above, but you can indicate in your own words that the rights of the host outweigh the rights of the guest here, and she should cancel and look elsewhere if she thinks children should be free.
You could get involved with Airbnb long before this situation gets to the point of them checking in and tell them that the guest is trying to bring extra guests for no charge when your listing clearly points that out.
Good luck.