After a gloomy period that has persisted for so long we've come to accept it as normal, last week brings forth an unexpected spell of brightness. It may be down to the brief reappearance of the sun, but whatever the reason, Joe Duffy takes a break from glumly carrying the weight of the nation's woes on his shoulders long enough to crack a joke.

During a discussion about mobile phone etiquette on Monday's Liveline (RTÉ Radio 1, weekdays), Duffy talks to Anne, a woman who recounts a visit to the cinema that was interrupted by another filmgoer's phonecall.

"I was going to see The Lord of the Rings," recalls Anne.

“Appropriately enough,” says Duffy, chortling away.

In any other setting, such a limp gag would hardly raise an eyebrow, but in this context, it counts as a torrent of mirth. In fairness, it also points to Duffy's otherwise underused wit, though given he hosts a phone-in show, he probably has a whole stockpile of telephonically themed jokes. Duffy's comparatively jocular mood is mirrored by the content of the show: stories about minor scams and the availability of GAA matches on satellite television count as frothy fare in the Liveline universe.

On Tuesday, however, the atmosphere clouds over as Duffy hears the latest grim tale of homelessness in Dublin. He speaks to Lorraine, who recently spent the night sleeping rough – or rather, staying awake in fear – in the Phoenix Park with her 15-year-old son, Carlos. Her experience is all the more terrifying for underlining how easily people can end up on the streets.

Having had to vacate the apartment where she had lived for four years (on rent allowance, but never in arrears) because the landlord was selling, Lorraine had then lived in a hotel since Christmas but was told to leave because her son had broken the establishment’s 10pm curfew. (He had been returning from his estranged father’s house.)

She then stayed in the bedsit of a friend who has a one-year-old child, but they all had to leave owing to rules prohibiting such dwellings being used as council accommodation.

Duffy sounds genuinely upset at Lorraine’s plight, but doesn’t neglect his usual tactic of asking a painfully obvious question to maximise the impact of a sorry story: “No one’s advocating bedsits, but was the bedsit better than the Phoenix Park?”

Perhaps stunned by the superfluousness of the query, Lorraine is briefly silent, before answering in the affirmative. She doesn’t want any special treatment, she adds, just to be “safe and warm”. To that end, she spent the two nights in the emergency department of the Mater hospital.

Duffy then speaks to Carlos, who reveals that his mother has Crohn’s disease; she is due to get an operation, but needs a home to receive proper aftercare.

As for Carlos, he has somehow managed to sit his Junior Cert in the midst of all this. He wants to go to college and make something of himself. At the very least, he says plaintively: “I want to have a house.”

Duffy is typically sympathetic as he draws out the young man’s tale, but when other callers voice their admiration for Carlos, the host cannot resist attempting some earthy humour.

“Carlos, are you scarlet?” the presenter says, in his best “down with the kids” fashion. It’s probably a more embarrassing moment for Duffy, but it’s as nothing compared to the shame one feels at living in a country where such scandalous situations exist.

Lorraine's case is not an isolated one. Over on The Pat Kenny Show (Newstalk, weekdays), the presenter hears from Amy, a mother of two who has had to sleep in a hostel while her children stayed in different locations. Kenny's interview is less emotionally raw than Duffy's, instead drawing attention to the systemic failings that lead to Amy's troubles.

Amy too had to leave her flat because the landlord was selling, but despite being given four months’ notice that she was leaving, the council was unable to help her find accommodation until she was actually out of her home. Increasing rents and the unwillingness of some landlords to accept rent allowance have led to her travails before she ended up in her current residence, a relatively high-end hotel.

Kenny largely downplays the human interest angle, perhaps wisely, as his one foray down the empathetic route sees him talking about Amy being “thrown out on to the side of the road”. (Luckily, her sensitivities don’t seem easily bruised.)

The presenter instead fulminates about the absurdity of local council housing rules and is perplexed that paying high hotel rates is seen as an ongoing solution for homeless families: “That cannot make sense.”

This focus on bureaucratic failings may lack the resonance of Liveline's emotive vignettes, but Kenny's attention to detail ensures the discussion goes beyond futile handwringing. And when the otherwise matter-of-fact Amy says she is at breaking point, Kenny sounds, in his own way, even more outraged than Duffy . "You are one among many – something has to be done." After listening to that, even the sunniest of moods would be darkened.

Moment Of The Week: Wicklow way with wit

In the Documentary on One: The Murderer, Me and My Family Tree (RTÉ Radio 1, Saturday) Dylan Haskins takes an ostensibly slim premise – a quest to discover whether he is related to John Haskins, the last man hanged in Wicklow Gaol in 1843 – and turns it into absorbing radio. Touching on oral history, identity, bereavement and memory, Haskins's search into his ancestry eventually leads to unexpected family connections. It also throws up some choice nuggets of Wicklow dialect. When Haskins asks farmer Pat whether there are any locals who might have stories about his long-dead namesake, he is met with wry indulgence. "You're a few year late coming," says Pat, chuckling at the notion.