I agree with @Iwishicouldflyhigh . If you like otherwise like the family, it may be worth thinking about this.
Of course it’s not your job to clean, but rather than thinking they are CFs and that their mess is a sign of disrespect, you could reframe it as them just being people who struggle.
It sounds like you’re a clean person. Are you good at cleaning, do you hate doing it or do you not mind? If you don’t mind cleaning, and don’t already have your next job lined up, and the job works for otherwise (commute, relationship with dc), then this could be an opportunity; Chip away at the cleaning, build relationships, have an impact on quality of life.
When the contract is up, explain youd love to stay, but it’s obvious they need a housekeeper/nanny. Say you’re happy to do it, but would need more money. This could be the start of a great relationship!
But, this only works if
You don’t mind cleaning/housework and would enjoy the challenge of having a bigger impact on their lives
You like the family in general
They don’t have any concrete child care plans in place for when your contract ends
They agree to a high enough rate 😁
I’m messy and it’s awful. Please don’t assume that these people are taking you for a mug - they are just very bad at keeping on top of their house. It’s not a moral failing, it’s a lack of skills. It’s not a power play over you, it’s probably just them in survival mode, balancing jobs, young family and possibly other things too (extended family, health, who knows?) Try not to judge and good luck with your decision