Maybe take the whole family on a mild weather event once the kids are old enough to enjoy it. Three of my fondest childhood memories of all time are: 1. My dad and I staying up to watch big Nebraska lightning boomers from a motel room all night long, on a family trip across country. 2. My mother discovered a rare lunar rainbow phenomenon was going to happen at the base of Yosemite Falls, so my dad and I got up at 2am to hike to it, and it was so great it was beyond belief. 3. My dad drove the whole family to a 10,000 ft. ranger lookout tower in the Sierra Nevada and photographed lightning.
Weather memories for kids are the best ones! If I was married or had kids, I would share my passion for weather and nature with them bigtime (it would be impossible for me not to because weather is so much a part of me I can't imagine being a non-weather person of any sort).
Maybe when they're older, your kids can help you take measurements, read data, and make observations and accompany you to a Skywarn class. Your wife might go for a weather expedition if she knew good memories would come. Right now, it sounds like her imagination is just running wild, fueled by what she sees on TV because she hasn't experienced even a little chase, when really, a lot of weather phenomena are quite safe and could become family adventures. There are many things to chase after as well, not just tornadoes (you live in Minnesota...you've got auroras to boot!) But if chasing storms is something you do safely on your own, then at least helping your wife to demystify it might help her realize you're not out there dodging John Deeres falling from the sky. Then each outing you get, she gets to do something she wants to do.