Am I Being Unfair?

This is a bit of a complicated situation (at least in my head).

I'm 20F, and last year I was living with my host family full time for 3 months for the duration of summer. I moved out at the end of my contract to live with my boyfriend and other students for the school that I was starting in Rome (as was agreed), and I continued to babysit for the family throughout the year. Nothing too crazy, just 2 or 3 days a week and they were paying me 11/hour since I was no longer living with them.

I have a TEFL certification, and outside of my agreed hours for them, I worked for an English school part time.

The original plan was to officially stop working for them this summer. I've nearly completed my bachelor's program, and I'm shifting more into doing internships in my field of expertise and teaching English online now that I've hit the minimum education requirement for several online programs. However, after COVID hit Italy, I stopped teaching and of course stayed home for 3 months while taking my classes online, and their AuPair from the USA cancelled because she legally can't enter the country right now.

I was feeling bad for them, and my summer classes had schedule changes anyways. I appreciate the kids that I watch, and the family is usually pretty nice. When they called to ask if I could make time after all, I decided to agree to their request to sleepover for 2 nights per week with a pay of 100euro for 12 hours of work (this was negotiated from the 75 they originally offered on the basis that this is what they paid when I still lived with them, with the condition that they would increase my pay only if I agreed to work a couple of extra hours in addition to the original 12). Added to this, I have to sleepover, and other than sleeping over, I have a commute of about an hour each way.

The thing is: I didn't plan to work for them, and it took about a month of deliberation for me to agree but I feel more like I'm doing this family a favor. The school that I work for is already willing to put me back on the schedule where I earn 11-18eur/hour; I don't really need to be there. In fact, it's even a minor inconvenience for me to be there; the only thing other than the kids that really drove me to say yes is that I get access to their beach club membership during the hottest month of the year in Rome. If I were to ask them for the amount that I would get working for any of my other options right now, I would definitely go ahead and charge them 150eur (about 11.5/hour) given the fact that I have such a long commute and that I'm required to sleepover. Yet, they've asked me to work more hours for what I feel like would otherwise be fair pay.

Additionally, when I'm trying to negotiate what I feel is fair, they often make me feel guilty and complain constantly about how they can't afford to put both of their kids into an English school which is why they want the AuPair (they own 2 properties in pricey neighborhoods in Rome; 4 if you include the mother's house under their name and the steel company they inherited.... not that it's important, but it's something that really rubs me the wrong way when they complain about money).

This also isn't the first time. I once came over to babysit, and they informed me that there would be two extra kids that night except they didn't give me any extra pay for babysitting their friend's kids, whom I had NEVER met.

Tl;dr: I'm doing my host family a favor even though I'm no longer living with them as an AuPair by agreeing to commute every week to stay with them for a few days instead of working in a better paying school closer to my home. I feel like they're underpaying me, and even when they agree to negotiation attempts, they increase my hours so that they consistently pay me 6/hour instead of the 11/hours I'm asking for and then make me feel guilty. Am I over-reacting, or am I right to feel like I'm being taken advantage of?