Hunter Biden arrived Monday for jury selection on a gun charges case that could prove an embarrassment to his father, Joe Biden, and hand a political weapon to Republicans desperate for a distracting issue in the wake of Donald Trump’s 34-count conviction last week.

Jill Biden, the first lady, also arrived Monday morning for jury selection at the federal courthouse in Delaware where her stepson is facing trial.

Prosecutors allege that Hunter Biden lied about his drug use on application forms when he purchased a handgun in 2018.

In theory, he could face a hefty jail sentence, but it is widely seen as highly unlikely. He has long struggled with addiction issues and a troubled private life.

The president’s son has acknowledged struggling with an addiction to crack cocaine during that period in 2018, but his lawyers have said he didn’t break the law. In his memoir Beautiful Things, he described becoming consumed by drugs and alcohol after his older brother, Beau, died in 2015 at age 46 from brain cancer. The brothers were very close, having survived a car crash when they were young that killed their mother and baby sister.

Related: Hunter Biden gun trial to begin next month after judge denies bid to delay

Hunter Biden has said he has been sober since 2019. But prosecutors intend to use his memoir to make the case that he knew he was addicted to drugs when he denied it on the form that every person must fill out when buying a gun.

A plea deal aimed at avoiding a trial collapsed last year, though it is possible some form of pact could still be revived as the trial starts to play out. But one thing seen as certain this is that Republicans will use Hunter Biden’s trial – and another more serious one over tax issues set for September – as a weapon to attack Joe Biden, as they have sought to do for several years.

Republicans will no doubt be motivated by Trump’s host of legal travails. The former president seen as a lock to be the party’s 2024 nominee was found guilty last week of falsifying business records linked to hush-money payments to adult film actor Stormy Daniels to cover an affair that was seen as potentially harming his 2016 election prospects. Like Hunter Biden, Trump too could face jail, though that also is seen as unlikely.

The timing of the trial is unfortunate for Democrats, who are seeking to highlight Trump’s historic first of being the only US president to become a felon. But Joe Biden, in keeping with his reputation as a close family man, has stuck by Hunter Biden through all his troubles and that is unlikely to change during the trial which is expected to last a week or so.

However, the trial could air potentially embarrassing family details.

David C Weiss, special counsel overseeing the prosecution, has signaled he will call Hunter Biden’s ex-wife, Kathleen Buhle, to the stand. Prosecutors also may call Hallie Biden, the widow of Joe Biden’s son Beau, who died of brain cancer. Hallie Biden was dating Hunter Biden when he bought a handgun in 2018.