I have a concealed carry permit so I'm covered regardless. However, some states (Ohio for example) say the firearm must be on one's person (i.e. in a holster) and in the glove box is a violation of state law.
It's a messy patchwork.
Your best bet is to get a valid permit from your home state, and carry the firearm in a holster concealed upon your person.
While I would feel much better with my .45acp, it's not a very easy firearm to carry totally concealed. That is why I opted for a 2" barrel Smith & Wesson J frame in .357mag caliber as my carry firearm.
The recoil is "stout" and it's not a very fun firearm to shoot. After 15 or so rounds at the range with full mag loads, I've had about enough fun for the day. Most of my range time with this firearm is with 38spl target loads. I probably run less than 100 full mag loads a year thorugh it. That is just to keep my proficiency with the arm up to snuff. I shoot in the neighborhood of 1,000 rounds of 38 spl rounds on a given year through the firearm while at the firing range.
My .45acp sees over 3,000 rounds on any given year
While one may not need to shoot as much as I do, if a person has a concealed carry permit, I believe they should put in enough range time to feel comfortable with the firearm. At a very minimum, you should practice to the point where you can keep 10 out of 10 shots inside a paper plate at 21 feet (7 yards). Even better, all 10 shots should be able to be covered by the palm of your hand.
Dedicated target firearms can do much better (1 big hole at that range) but most concealed carry type self defense firearms have poor fixed sights, short barrels, fairly stout recoil due to the light weight which results in a 1" - 2" group at 7 yards is a pretty decent day shooting for most of us.
Also, always wear eye protection while shooting and don't do as I did in my younger years and skip the ear protection. ALWAYS wear proper ear protection while at the range. I can assure you that you don't want to end up with the kind of hearing loss I suffer nor do you want the constant companion I have of a ringing in my ears (that is about the A# note on my guitar, at least I can use my buddy the "ear ringing" for something useful while tuning a guitar).