Is it possible to work from my parents' home on a postdoc?
Only your school and your department and your group can tell you what their expectations are. Ask them.

But face-to-face networking with others is hugely valuable both for your current tasks and for being aware of new opportunities,, and think carefully before you give that up. I've been working from home for about 5 years now (commercial, not academic), and it has definitely cost me in terms of career progress despite my making deliberate efforts to stay in the loop.