Hmmm - I am on the fence on this one. I will preface this by saying that I have owned and used both shotguns and rifles, for more years than I care to remember, for target and live quarry shooting. I make no apology for that; the morality and ethics lie easy with me. Other people are, of course, entitled to a different view, provided they do not try and force that view on me! Ownership of and an interest in guns and shooting does not make one a 'disgusting' person, a psychopath or a mass killer in waiting - of course it doesn't. I regard a gun as simply an inanimate aggregation of wood, metal and, in some cases (ugh), plastic.A tool to carry out aspecific task. The purpose and intent of the person behind the trigger is what changes the dynamic.
I am, however, very surprised at many of the responses which the OP has received here. She, (assuming the OP is a woman, since a husband and children are mentioned) has outlined a very strong revulsion toward guns, mentions trauma, but has not disclosed, as is her prerogative, the nature and extent of that trauma. For all we know, purely speculative and conjecture, of course, she could have grown up or lived in a war torn country, or one riven by civil war or unrest. She may have witnessed atrocities which most of us could not even begin to comprehend. In which case, her antipathy and aversion toward and hatred of guns would be more than understandable. I doubt that councelling or therapy could ever help with that! Or maybe not - there may well be another strong and valid reason why she feels as she does - it is clearly a very entrenched opinion.
In this instance, if her husband is aware of why she feels as she does, my view is that he should gracefully back down - is it really worth tearing the family apart for the sake of persuing what may well be a short lived hobby. The OP's opening post suggests that her husband tends to flit from one short lived hobby or obssession to another. As a compromise, there ARE ways he could experience and indulge this new found hobby, without rushing into aquiring a shotgun or firearm certificate and bringing a gun into the house, which clearly would distress his wife beyond measure. I would not dream of imposing such insensitivity on my partner, if it was so contrary to their wishes, views and feelings.
I must also take issue with those who have suggested that air rifles are 'toys' or not 'proper guns'. Even a low powered air rifle is more than capable of blinding someone, causing other life changing injuries or even death - there have been cases of fatalities caused by air rifles. And any air rifle with a muzzle energy of 12ft/lb or above is classed as a Section 2 firearm, is bound by the same certification and security requirements as a rim fire or centrefire rifle. Never, ever regard an air rifle as 'not a proper gun'. They MUST be treated with the same care, respect, safety awareness and due diligence as any other firearm.