Vehicles have safety ratings from the government and insurance companies, and despite some artificialities vs real world, they are pretty good metrics.
Wranger is obviously going to be pretty low for a half dozen major reasons both in a) what happens to passengers in a given accident and b) ability to swerve, brake etc in avoiding an accident in the first place. rollover risk, airbag numbers, generally high speed handling, suspension, protection at side impact, etc
So if the questions are:
"Are my kids in more danger in a wrangler than a top safety rated car if hit by another car?" or
"Are my kids in more dander if the vehicle in front slams on brakes at high highway speeds and I have to swerve attempting to avoid"?
Th answer to both is yes, they are in more danger.
So if your only concern is safety, all other things equal, the wranger is not a good choice.
But also be aware that any bike riding, sledding, skating, skiing, swimming in pools, lakes and the seashore are also all very dangerous for kids
Moreover behavior while doing those things -- and jeep safety -- is the major determinant. It is not so much the activity, but how you do it. Vehicles accidents are largely determined by what you are doing. With increased safety features vehicle fatalities should be dropping -- but they are not. Why? Texting. Like owning guns, for the data set of all people owning one increases danger, while for the data set of people not engaged in crime. The high self created behavior based risk group driving most harm, up to 90%, is a group taking a secondary risk (engaging in crime) and for most people it likely does not increase risk at all.
if you really want to reduce risk driving,look at other risk factors and leave your smartphone at home. in a jeep with ABS, ESC, airbags you are safer than virtually any vehicle from 25 years ago if you are an engaged non-distracted driver
The fact is being in a jeep is fun. And like most fun outdoor activity it has an element of increased risk.
if your wife is really worried, have her get a top 20th percentile safety rated vehicle, to drive your kids around the majority of the time. when they are in the jeep have them enjoy it, knowing like bike riding, there is some increased risk