I think it's highly weird. It would make me think that she and I have very different definitions of "pet sitting" and boundaries and I'd wonder what other things she thought she could do at my house without asking: rummaging through my medicine cabinet, going through my closet and borrowing my clothes, reading my mail. I'm not saying she's doing any of those things, but if we're on such different pages about "letting the dog out when I'll be home in a few hours" what other definitions do we differ on?
We had a neighbor who would pet sit for us when we went out of town. She specifically said to me "Generally, when I pet-sit, I stay at the person's house. Is that ok?" I didn't want her sleeping in our bedroom, using our sheets, necessitating laundry for me and an immediate changing of the bed sheets when we returned home from a long flight. I told her not to stay at our house, just to come X amount of times, open the door for the dog to do his business, let him back in 5 minutes later and that's it.
Before we left, I emptied the dishwasher. When we returned, some of our dishes and silverware were in there. There were paper bags in the trash from various restaurants. It was obvious she'd eaten numerous meals at our house on our dishes. There was even a drinking glass from a restaurant (it said the restaurant's name) that I'd never seen before. Our sheets look slept in. Some of the towels looked used. She didn't live far away and there was no reason to be sleeping in our house especially since I had told her not to. Based on some of the things that had been moved near the sofa, I suspected she had at least one other guest over. Nothing was missing, but it made me very mad. After that, we never asked her to pet-sit again.
ETA: correct conjugation