AITAH for paying my caregiver our normal daily rate instead of $25/hour for an extra day she worked?

I privately hire a weekend caregiver for an elderly lady. Our standing agreement from the beginning has always been $350 per 24-hour day (Friday evening through Sunday evening). It has never been an hourly job.

A while back, she couldn’t work one weekend because she couldn’t find someone to watch her dog. I really wanted to keep my Saturday morning plans, so I asked if she could at least come for a few hours Saturday morning.

I asked her what her hourly rate was, and she said she didn’t really have one. I offered $25/hour for that specific situation because I really valued having that Saturday morning free.

These are the actual texts:
Me:
“How much is your hourly rate?”
Her:
“I don’t really have one.”
Me:
“Ok. How about $25?”
She agreed.

Later, while we were still discussing that same weekend, I also texted:
“I’d pay for the Saturday night 9pm–9am ($175) and any extra hours, I can do hourly $25.” She declined as she wanted the weekend off anyway.

After that weekend, we went right back to our normal arrangement of $350 per 24-hour day.

Fast forward to recently. She offered to work an extra 24-hour day because she was going to be out of town for the Fourth of July weekend. I understood this as another flat-rate day under our normal agreement ($350).

When it came time to pay her, she expected me to pay 22 hours × $25/hour (about $550) because she believed anything over her normal 48 hours should be paid hourly (she told me I told her this)

I was completely surprised because I thought the $25/hour was a one-time arrangement for that specific partial Saturday shift when she couldn’t work the full weekend due to her dog.

Also, she had told me before she was thinking of quitting her main job to come work for me extra hours. I clarified then, I wouldn’t be paying $25/hour, I told her that it was a special rate for her because I wantes that Saturday morning off.

Anyway she got offended but said she wasn’t going to fight about money. We ended up talking it through. I paid the normal $350 for the extra day, apologized for the misunderstanding, and we agreed that in the future we’ll always confirm pay before any extra shifts.

The next day, she told me she wasn’t going to be working all wekends for me anymore and she will be cutting back to every other weekend only.

AITA for thinking the $25/hour offer only applied to that one weekend and paying our normal daily rate when whe worked the extra 24 hours?