I think I’m being taken advantage of

I started a nanny job through Care.com during a time when I was desperate for work. I care for three children, ages 7, 9, and 12. Originally, I was hired to work from 2:00–5:30 p.m. every weekday after the kids got off the bus, including picking one child up from school each day. My responsibilities were to supervise the children, clean up any messes they made while I was there, and prepare them a proper dinner so their parents wouldn’t have to after work.
Over time, the job has expanded significantly. I was expected to start taking their dog on walks, feeding him, cleaning all three children’s bedrooms, sorting through their clothes to determine what still fit, doing all of their laundry every week, cleaning out the refrigerator, and organizing the pantry. I’m paid $20 an hour with no gas reimbursement, despite driving for the job.
The schedule also makes it nearly impossible to find another job because the hours fall right in the middle of the afternoon. I only make around $220 a week, which isn’t enough to live on.
On top of the growing list of responsibilities, the children are extremely difficult to manage. They regularly refuse to do homework, won’t eat their meals, won’t help with basic chores like walking the dog or cleaning their rooms, and often expect me to do everything for them—even asking me to bring them a straw for their drinks instead of getting it themselves. They fight constantly, sometimes even pulling each other’s hair. They are spoiled rotten. Like every Sephora product spoiled. Like so catered too it’s almost disgusting. These children will be useless adults.
One example happened today: the 9-year-old picked up my brand-new Birkenstocks after I had told her they were new and expensive. She threw them around the house, put one in the dog’s mouth, and tried to encourage the dog to chew on them, because the dog is known to destroy shoes. It felt like she was intentionally trying to provoke a reaction from me. Incidents like that happen often, and all three children sometimes seem to antagonize me just to get a response.
I also know the family is financially very well off. My mom’s did research on the family and discovered. The mother is a vice president at a food supply company, 800,000 salary. and the father is a director at the same company, 400,000 salary. While I don’t expect their income to determine my pay, it is difficult knowing they frequently travel to Ireland while I earn only about $220 a week. Whenever they return from vacation, I’m expected to unpack all of the family’s luggage, wash all of their clothes, and put everything away.
When I stopped deep-cleaning all three children’s bedrooms, the parents politely asked me to continue. When I skipped walking the dog one day, they reminded me that they preferred I handle it because they didn’t want to deal with the dog after work.
I’ve now worked for this family for a year. They tell me they really like me, and I have a good relationship with the children despite the challenges. However, a bridge I use to get to their house is under construction, turning what used to be a five-minute drive into a twenty-minute drive each way, and the construction is expected to last until next year.
Because the responsibilities have grown far beyond what I originally agreed to, the commute has increased, and the inconsistent afternoon schedule prevents me from taking another regular job, I no longer feel that my time is being fairly compensated. I’m considering asking for a guaranteed weekly minimum of $300 and am wondering whether that would be a reasonable request.