I am really very sorry Jae that your stay with us was, in some ways, unsatisfactory.
I have today amended the description to make it more explicit to future guests that the apartment is within our family home. This was stated originally on the description but I very much take on board your feedback and will make it clearer.
As our home is over four floors, and the apartment is in the lower half, we always ensure that the children are kept away during the evening and mornings, so that guests sleep is never disturbed. However, as you correctly state, they are young and so some noise during the day is inevitable. I hope that future guests are fully aware of this as a possibility and are able to take this into account when booking. We would hope that guests are able to bear in mind that our listing embraces what in my view was Airbnb's original guiding principle of providing relatively low cost accommodation within people's homes.
I have today messaged the Airbnb help centre to enquire as to how I can offer you a refund and hope that this will compensate for your disappointment.