The dilemma is how to fix this when the US is saturated with guns. The gun nuts are right, people are still going to have a shitload of guns because they've been allowed to have a shitload of guns forever. It's kind of bullshit, Europe has all this cool stuff like gun control that curtails violence and awesome prisons that curtail recidivism but our system's been shitty so long it wouldn't work here because we have so many guns and such a strongly recidivist prison population.
I don't think US gun culture and prison recidivism are related. The recidivism rates in the US are as high as they are due to a combination of prisons lacking rehabilitative programs and the extreme social stigma placed upon everyone who has ever been imprisoned, precluding them from any way of making money other than more crime once released. These factors are not helped by prison privatization, which puts the prison system in the hands of a structure who's primary concern is not lowering recidivism but making profit. Furthermore, the War on Drugs has allowed organize crime to flourish in the US, and the social structures provided by these organizations are all some prisoners have ever known and will ever have in prison or out of it. It's a virtually inescapable trap. If you wish to curtail recidivism, don't bother with gun control because that won't make any noticeable dent. All that will do is somewhat change the tools of the trade without stopping the actual trade, and lead to way more arrests as US gun culture goes down fighting. We do not need more arrests. The prisons are already critically overcrowded all the time.
To reduce recidivism rates in the United States of America:
-Nationalize the prisons, because sweet fucking god we are going to get nowhere fast until that happens.
-Legalize all soft recreational drugs and regulate them for commercial sale, decriminalize all hard recreational drugs and put users in rehab instead of behind bars. Watch as organized crime in the US and the world over collapses in a power vacuum as corporations provide cheaper and safer product to soft users and rehabilitation takes away hard users, destroying criminal profit.
-Legalize and regulate prostitution, Nevada or Germany style (doesn't matter, really), to further reduce criminal profit to end another avenue of victimless crime generating new prisoners.
-End Three Strikes Laws in states that have them and re-sentence all prisoners under the third strike to a proper term, releasing them if exceeded. Who the hell thought Three Strikes was a good idea in the first place?
-Provide maximum security prisoners with known gang affiliation identity protection and with sustained good behavior the chance to be transferred to medium security if they renounce gang affiliation and provide information to prison officials. This wouldn't work too well on its own, but with organized crime hurting as it is due to drug legalization by now the gangs will be at their weakest and vulnerable to conversion.
-Cease the practice of the Death Penalty. The death penalty's moratorium never should have ended in the first place so this is just more of a general reform to bring US justice up to speed, but states with the death penalty have higher murder rates than those without, so it might help.
-Cease the practice of Solitary Confinement. Even putting aside ethical issues, solitary confinement is the opposite of reform inducing. People need to be around other humans, even if it is trivial or unpleasant. Putting prisoners in solitary confinement for weeks just makes them vengeful and mentally ill, not a good idea.
There is more than could be done than that, but this addresses the main problems.