Please help-- disrespectful nanny family

Update: Thanks for all your help! I knew that this position wasn't going to last much longer generally but this situation has made it clear it may be over sooner than I thought. I'm typing up a draft of a message to send and will update here when I hear back from them. I really struggle with firm wording with my employers and this has been really helpful!

TLDR: very wealthy family is nickle and diming me and treating me like the "help" how do I fix this??

I'm anonymizing a lot of this info as I'm pretty sure my NF is on reddit. I live in an incredibly HCOL area on the west coast and have over 15 years of experience nannying and have never experienced anything quite like this.

I have been with my current NF for a little under a year. I take care of their two kids, one school age and one toddler. I have a lot of qualms with their parenting style ie. letting the baby cry it out for over an hour without going into the room AT ALL and never telling their older child no/letting him manipulate them as to not "hurt his ego". Mom has also made comments about my weight that are incredibly inappropriate and it feels like she is always trying to squeeze whatever she can out of me. They are constantly nickle-and-diming me and it's starting to really take a toll. The family is incredibly well off, ex. School age kiddo is in day camp this summer that's almost 2k/week on top of me taking care of the baby full time.

This is all coming to a head now as we're preparing to go away for vacation. my NF has in my contract that if I go away with them I have an extra week of PTO. I sent over a formal travel contract that included a nightly fee for travel as well. They are saying that my extra week of PTO is the travel payment (on top of my normal guaranteed hours pay). I have traveled with many families and have always required my own hotel room, either on a separate floor or in an entirely different location (ie family stays in an air b&b and gets me a hotel) in addition to a $200/night travel fee. I have also always been paid OT rate for all time spent on the plane or driving to the destination, regardless of whether I hit 40 hours on the trip because caring for a baby on a plane deserves 1.5 pay. I have never had a family question me on this.

This family wants me to stay in the same house with them and not pay the overnight fee. I'll also have baby on the plane (6 hours) for my normal rate. I assumed that the week of PTO was in addition to the overnight fee to make up for the lack of things which are standard in this area. I have talked to many other nannies in the area (I have a large network after working here for so many years) and they all think that my NF is trying to grossly underpay me for this trip. I am trying to figure out how to either get them to understand that they are underpaying me or get out of this trip all together.

Any help is so appreciated and I'm happy to provide more context if needed.