Thank you for your feedback. We appreciate any review that helps us improve our service, however please consider the fact that you choose to book a ticket in advance and not on spot because you wanted to be sure your seat is guaranteed before arriving at the lagoon - hence the very small price difference.
Usually entrance tickets are sold out so driving there just to not be able to enter the lagoon is not something very pleasant. So paying on spot can be possible if only there will be availability.
Children are free, just like you booked. You paid only the ticket adult.
Hope you had a great time in Iceland and looking forward to welcome you back!