@Liz3810 No, it is not acceptable for a host to enter the rental space without prior notice, arranging for a convenient time, and that should only be for some serious situation, or some necessary regular maintenance, but even that should be made clear when booking. The only time it would be acceptable is if there was an emergency, like the place was on fire, or the host saw water pouring out somewhere. I host a private room /bath in my home where I live, not even an entire self-contained unit, and I never enter the guest space at all during their stay.
This host sounds nosy- like she's checking to make sure you're being respectful of the place. The "weird smell" story sounds bogus. If there was a weird smell she noticed when preparing the place for you, she should have mentioned it, and asked you to contact her if you detected it as well.
If I were in your shoes, I'd message the host and say something like " Hi XX- it makes us feel quite uneasy that you would enter what we booked as an entire private home when we were out. We have an expectation of privacy here which has been violated. If you need to come over for some maintenance or repairs, we expect that you will notify us first and arrange a convenient time for both of us and please never enter when we are out. We are respecting your home and expect the same in return."
If she continues this sort of behavior, you may have to consider whether it's worth completing this stay or not. She probably means no harm, maybe she's had issues with guests trashing out the place before, likely just a Nervous Nelly, but in any case, her actions aren't okay nor at all professional.
