Hi there! Long time lurker, first time poster - hope this comes out right . . .
In general, judges do seem to have little in the way of free time and a private life. Dredd certainly devotes himself to the Law 24/7, and only recently has he started taking time out to do "nonjudicial" things - witness the reintroduction of his niece Vienna into the comic strip.
However, Dredd is notoriously and possibly uniquely rigid in his conduct, and other judges do seem to find some time for themselves. I don't have the prog numbers to hand, but I seem to recall a story in the Megazine in which Hershey takes time out to accompany her young nephew to a circus (I think the story featured a harlequin-like character who kidnaps children). Of course, that was before she became chief judge. Nevertheless, this story, like the recent one in the Megazine where Giant meets with his grandfather, John Clay, does illustrate that judges can take some personal time (and may choose to spend it with family members).
There was also an old Anderson story where she and the late Empath Corey change into civilian clothing and go nightclubbing! The story is reprinted in one of the Anderson collections (and by the way, does anyone ever get the feeling that Psi-Div operatives are really coddled by Justice Department? Any time we've seen Anderson's quarters, they seem a heck of a lot more comfortable than the typical street judge's accommodations. And she has a Dredd plush!)
A third example - there was a one-shot story (illustrated by Ian Gibson, if I'm remembering this right) where Dredd is on a mandatory 24-hour rest period but can't sleep. He isn't allowed back on patrol, so he ends up in a bar near a spaceport, where he shares a (nonalcoholic) drink and a chat with some decent citizens, including an Apocolypse War vet. I think that story refers to some sort of new policy encouraging off-duty judges to interact with citizens, but I'll have to dig out that prog to see if I'm recalling that correctly.
Way, way back when the Dredd strip first began, we often saw Dredd in his apartment in Rowdy Yates block, interacting with (i.e., being exasperated by) Walter and Maria. I suspect that prior to the Apocalypse War, judges probably did have more free personal time. Since then, MC1 has been hit by major disasters (the war, Necropolis, Judgement Day, the events of Inferno, etc.) on a fairly regular basis, and it has been mentioned several times that Justice Department is undermanned, which has probably led to a scaling back of the amount of down-time afforded to judges. Plus, given their sense of duty, many judges probably choose to forego any leave they might accumulate, spending it instead dispensing justice on the streets.
It's also been mentioned in one or two stories that Hershey's reign as chief judge is somewhat more liberal than those of previous chief judges, so if you want your PC judge to have more off-duty time, you could frame it as being part of a new experimental scheme whereby judges are given an opportunity to better understand the citizens they police by interacting with them on a more personal basis.
In the campaign that I play in, my psi-judge keeps threatening to take the street judges in her new squad out dancing in a nightclub. I don't think they realise that she's not joking . . .
I love Psi-Div - you can get away with sooooo much stuff that would have a regular street judge booted off into traffic control.