“I rent a home and my landlord just rented another home next door to me. A tree fell and almost hit his new tenants car, so now my/our landlord said she is allowed to park/use my driveway, which is not part of her home, it is on my property. Can he allow her/anyone to park in my driveway and upset my privacy?”
Technically, neither the driveway nor the home is “your property”; it still belongs to your landlord. What you have is the right to use and possession of that property for a period of time.
So the first question is, what does your rental agreement say that you are renting? Is the driveway actually included in what you’re renting, or are you just renting the home and have an associated right to park?
Assuming that your rental includes the driveway then no, your landlord does not have an unfettered right to use (or let others use) it. You may be willing to accommodate your landlord in this unusual circumstance, but that would be up to you and any agreement you and your landlord come to.
If it comes to that (and I’d try to avoid this, for obvious reasons) you may need to consult an attorney to enforce your rights against your landlord.