So I started my part-time PhD in December and it is now Easter vacation - how should I spend the time?

I think you should have a nice holiday with your family Jepsonclough, as you've been working very hard. :-)

Yes, Jepsonclough, the holiday with the kids sounds like a top idea. Don't mark the undergrad essays, we at PGF have proven evidence that undrgrad essays are contaminated with a mind numbing and zomifying virus, They made a tv series about it: Did you ever see Survivors on BBC2? Well, it was based on true life PhD experiences, so I'd head for the countryside if I were you.

As long as it won't stress you out or seriously mess with your deadlines, then chuck the laptop in a draw and have a holiday! Apart from anything your family will really appreciate it. They're more likely to support you through the years of phd obsession if they get little packages of time where they come first.

Take a break, you deserve it :)