I carry mine unloaded in my bike bag and the cops said that is fine. I think it is only a problem if you can reach it while driving. That's the case here anyways. Too bad we don't have concealed carry. Then it wouldn't be an issue at all. Be glad your wife is a good shot. My wife is a horrible one. I have told this story on here before, but here it is again:
My wife and I decided to fire off some rounds at the indoor shooting range I frequent. We always take turns shooting. Then, while one shooting, the other can reload the clips. The range I shoot at has an automatic retrieval system for the targets. The downside is, the targets are only held on by a cheesy clip thing and they frequently fall off as they are being flown into position. They have a v-shaped piece of steel that covers the clip thing so that you don't shoot and destroy the clip. It is v-shaped, so if you do hit it, the bullet will still stry downfield. A lot of experienced shooters at this range will reverse that v-shaped pice of steel to provide wind protection for the target. This is really stupid to do however, because then that V is reversed and instead of sending the bullets down range, it will send them right back at you. I see them reversed all the time but think nothing of it because I have never even come close to hitting one. I am a pretty good shot. My wife on the other hand.... Well, she squeezed off a few rounds and suddenly I felt something whiz by my head heard a "cracking" sound in the wall behind me. I yell for her to stop and turn around. Sure enough, one of her rounds bounced back and entered the wall behind me. After cleaning my pants out, we retrieved the target and saw that she had killed the cheap ass clip thing and that the V-shaped piece of steel had indeed been reversed. The scarey thing is that the shooting carrols are only about 3 feet wide and we were both standing that area. I was behind her and off the to side a bit, watching her shoot and reloading clips. So we were taking up basically the entire space and the bullet still seemed to miss us both. I had a chat with the owner of the range and since then, all of the v-shaped pieces have been welded into place. My wife was a little scared to shoot again, but she has been back several times and her shot has increased dramatically.