That resonates a lot with me. A few years back my manager in a big-co with a lofty motto would not allow me to work remotely for a week or two to stay closer to my dying parent. As she pointed out, "a lot of innovation happens at the watercooler".
This was cruel and there is no excuse why in 2016 this arrangement couldn't work for a week or two.
As a remote member of a mostly onsite team there is some validity that you miss out on the SOCIAL aspects of work (grabbing lunch, hanging out after work from time to time, etc) but the "innovation" on our team is just fine.
But of course, you don't want to work for someone like that in the first place, if you can help it.
This won't last forever—enjoy it while you can. Say no early, say no often!
It'd be reasonable to say something like "We had different perspectives on the structure of the workplace and it just wasn't really what I was looking for". They'll probably ask "Oh, what was the issue?" and you'll say "I needed to work remotely to be at the bedside of an ailing parent and they said they'd fire me if I tried, so I quit".
You don't want to look like you're blaming them for making you miss your parents' final moments (we're grownups and take personal responsibility for things like that, don't allow people to stop you from participating in important life milestones), which is why it's a good idea to allow them to dig a little bit before getting at the real dispute. This is a good principle when discussing previous employers anyway. You always want to sound like you're over whatever the slight was, that you see and understand their perspective and don't blame them for having it, but simply don't agree with it. You won't be faulted for that.