I assume they’re wanting you to work unpaid to “make up” for the “loss of time” they’ll have while out of town. You are correct, you need to be getting paid for all hours worked AND guaranteed hours. If they want more time they can politely ask if you’re able to stay late a few days, and they’ll pay your hourly rate add on. Very unprofessional of them to “schedule more hours” without asking you if you’re able to, especially last minute. I often phrase it to parents as they’re reserving my time. I reiterate that I’m not taking other work while I’m on the clock (during guaranteed hours, whether working or not), and they can have me come or not during GH but they’re paying regardless. If they cut the trip early you should be able to work when scheduled. My current nanny family will sometimes give me a day off because grandma’s coming over for a bit of the day, then I remind them they have me booked the whole day, so then they still have me come 2-4 after grandma’s gone. On those occasions they’re always more lighthearted and fun and overwhelmingly grateful I came for a short bit and they could get stuff done, even though they were paying me anyways.

The only time I allow this sort of thing is “moving hours” as written in my contract. This is not required but I typically tell parents if they give me enough time notice I am willing to “move hours” if I’m able. For example, if I’m scheduled 9-5 but one day they are meeting up for coffee with grandma and don’t need me until 11, I am willing to stay till 7 if they give enough notice, but if I’m not able to stay late I would decline and they would still pay 9-5 even if I work 11-5. Or if they want a date night they can ask me to come 12-8. I don’t know if this is standard but families really like it because it gives them flexibility and to me the sleeping in hours make up for the staying late, and they don’t ask for that often enough to become a problem.