Does paternity leave actually exist or is it just a thing HR talks about?
Used up my official "paternity leave" (2 weeks, corporate job, major city). Half that time I was still answering emails because "things came up." Could my boss legally require that? Probably not. Did he ask real nice and make me feel like I should? Yeah.
Looking at new jobs partly for this reason. Somewhere that doesn't say they value fathers being present but actually means it.
The fact that you were working half your paternity leave says everything about how this country treats new dads. That's rough man.