Cheapest ways to stay in Oahu with a family

My family is going on vacation to Oahu from December 30th to January 12th and my mother is super stingy and isn’t willing to spend over around 5,000 or 6,000 dollars on where we are staying. We would need space for 7 people and my mother is adamant on booking somewhere with a kitchen and at least one private room for her and my dad. I’ve been looking everywhere and can’t find anything for that cheap that meets her expectations. I’ve told her it’s unreasonable but she is convinced we will find somewhere. In an attempt to somehow appease her I wanted to ask anyone of any methods or ways they’ve stayed on Oahu with a group around that size for that cheap with the amenities that I’ve talked about. Please tell me anything, even if it’s unconventional! Willing to look into anything and we are fine to stay just about anywhere on the island.