It's a very nice neighbourhood and my parents' furniture is expensive.
However, furniture thieves are more likely to target castles or museums (it happened) and frankly, the neighbours would notice a moving van in the middle of the night!
I feel like you need to take a hard look at which of these concerns and expectations are reasonable and which are unreasonable. Your parents presumably live in this house, unmolested, on a regular basis. Property thieves and vandals are a realistic worry for anyone, I know, but it seems like your parents have an extreme concern about this, which doesn't seem to have a realistic basis in fact and likelihood.
Steal stuff, steal furniture, break furniture? So you need to stay and protect the house. But then someone needs to stay to protect you? How can it possibly be so dangerous for you to stay the night there if your parents live there (safely)? And is it really likely that your parents' house would be an instant target for furniture thieves/vandals and people who would attack you in the night, if, like you said, this is a 'nice' neighbourhood?
If I were you I'd take a long look at what fears are grounded and what fears are more habitual and ingrained by exposure to years of your parents' beliefs. Being this worried because it's a detached house really doesn't sound reasonable to me.
ETA: What I mean by this is that it's helpful in distinguishing what your parents NEED versus what they WANT. They *want* you to stay in the house and your husband to stay in the house because it helps quell their anxieties. But I'd argue that they don't *need* you to do these things in order for the situation to be safe (as safe as any situation can be - life has risks.)
I find it very difficult when people create needs out of wants, because it then seems to give them a firmer basis to demand that you acquiesce to their wishes, pressuring you not to deny them something they *need* ...when really it's just something they want you to do.