What you are experiencing are the same doubts and insecurities that virtually everyone has when first considering becoming less auto dependent. But just like everything else, you make the adjustment over time until it becomes routine.
I've seen a lot of good advice here.
I also recommend the AAA option. If nothing else, it helps save on the price of many hotel rooms when you travel whether you drive, fly or bike. As for roadside assistance, I've found we rarely use that....I think once in the past 10 years and that was due to something stupid on my part. (Way too embarrassing and I'm not even going to go there.) Certainly not worth the expense of a second "just in case" car. The chief benefit of AAA is knowing it's there if I need it but hope I never need it....sort of like the local Fire Department. If you want the security of a second motor vehicle, consider something besides an automobile. My wife and I have a little Italian Vespa scooter which could serve in a crunch. But at only 400 miles in the past two years, it's more a fun way to spend an evening out together than anything else.
Remember, car free or car light is making the adjustments necessary to make it possible. It would be difficult if not impossible to become carfree yet continue to live a car dependent lifestyle. Sometimes it requires thinking outside the box. It never ceases to amaze me how many cyclists we have in my area that routinely ride 50+ miles on any given day, go home, shower and then drive six blocks to grab a sandwich. It never even occurs to them that the bike can be used for something besides a recreational ride.
My wife and I have found having one car - really only for her as I very seldom use it - is plenty sufficient for our needs. We dropped from three cars to only one about six years ago and I can probably count on one hand the number of times we had conflicts for needing the car...and even then it was more a convenience issue than a true need. (FWIW, my office is 25 miles from my house so its not like I can simply choose to walk to work. Luckily, I have good transit service which makes my commute simple.)
If you really want to go car light, then give it a genuine try. Just remember the first few months will be the toughest until you figure out the routines, etc that make it work. I for one have been very happy with the change ever since my wife and I did it and can't imagine ever going back to having two cars. Heck, I'm leaving for ten days in Romania next week just on the money saved so far this near by not having a second car.