Most of my belongings remain in what is still my house. Whilst my ex husband is happily living in the large 4 bed detached I have a tiny flat that simply cannot accommodate anywhere near all of my things.
I don't think anybody is suggesting that you move everything you own into a tiny flat, but surely you can manage without having to go back multiple times per week for - as you say - clothes, shoes and handbags? I think any reasonable person would see this as excessive. If you take as much as you can manage, even if its only enough to last you for a few weeks at a time, you're limiting the time you need to be in the house to however long it takes to do what you need to do for the dog.
I am still firmly of the belief that there are hidden cameras or recording devices, probably hoping to catch phone conversations when I sit with the dog in the lounge for a while.
If you're 'firmly of the belief', then don't have telephone conversations when you're sat with the dog. Take the dog out and have those conversations, or have them at literally any other time.
You're not taking anything you shouldn't, there's no conversation for him to 'catch', he's literally wasting his time. You shouldn't have to do this of course, but given there's nothing you can legally do about any cameras, what other outcome are you hoping for?
You say that he's doing this purely for vindictive reasons, yet you're willingly, repeatedly putting yourself in positions for him to exert his influence on you because...why?
You need to figure out what's more important to you. Finding excuses to visit the house every other day 'just because I can', or him not having the satisfaction of spying on you. You're in a tremendously difficult situation, but there are some very easy short term steps you can take.