Hope you gave him an earful!
He was very nice and we chatted but I didn’t invite him in.
That’s lovely, I just meant that he probably needed to be informed that he wasn’t supposed to be there. Did he not know where his mother was? 
Yes, I think he was asked to check up on me.
As an HS, I’d have no issue with an HO maintaining their dog’s normal routine.
That dog walk may include training, structure socialising with a known group of dogs, a myriad of other things…being there as a sitter doesn’t mean that everything else in that dog’s life stops, especially if the other thing is a special skill set.
The sister dropping in?..yea, Idk about that one. I agree with others that you’d have to decide if you’re comfortable with that as it could affect liability of things if an issue were to arise, but if it’s quality time with a loved one that the dog is used to, I’d probably just use that time to leave and also to clarify that, while one of their people is in the space, liability and care of the dog is on them for that time frame and then to make sure it’s set to a consistent or known schedule…that’s just me though…ultimately, you need to do what you’re comfortable with…TLDR, I’d try to keep to the dog’s normal schedule as much as possible without compromising what I’m liable for/uncomfortable with.
Re: other types of pop-ins…as HOs we do have service workers and deliveries/pick-ups that we ask the sitter to help us manage, but we do our best to give as much notice as possible and if something can be moved to a time when we’re back, ofc we will try to do that, but for me as an HO/HS, I personally believe that the HS is meant to be a proxy for the HO in their absence and pop-ins of this nature are part and parcel of taking care of the house, just as managing the pet’s routine is part of taking care of the pet.
Maybe it is a dog with separation issues and high anxiety and the HO is simply trying to make this work for the sitter. To me it would be worth communicating with the homeowner. Of course the sister shouldn’t be “popping in.” But maybe the sitter could use the sister’s number for emergencies or so the sister can take the dog for an afternoon if the sitters want to go do something without the dog. This is worth a conversation and maybe a negotiation to reach a comfort level for both parties.