Texas and the puppy

First, let me say I adore my puppy. I honestly think she is a wonderful dog and very much like a first child to us. It did my heart so much good to see her run and play int he backyard when we moved here- she hasn't ever been able to play like that. She loves just running in circles in the backyard. She keeps me company each day as a I work, starting the morning by sitting on my feet til they are warmed up, then moving to a sunny spot in my room and napping, moving every 15 minutes or so to keep up with the sun. Here is my desk- note the puppy curled up on the floor:

But the last few weeks have not been kind to her. First, there was the adventure of last week- I was in my office watching her from my window, running in circles and playing with invisible tennis balls or something. My office window only covers about half of the backyard, but she makes such big circles that she comes and goes from my view pretty regularly. And then, once, I looked out the window and... no puppy! I go downstairs and look outside... still no puppy. I go outside and look under/behind everything... still no puppy. Just a gaping obvious hole under our fence we hadn't noticed before (Lucy didn't dig it, we're just dumb and didn't check the perimeter of our fence for such things).
Now, I've lost dogs before. With Chester, the dog of my youth, it was seemingly a weekly occurrence. Chester, however, was a street-wise dog and knew that cars are not our friends. Lucy, however, just sees something big and fast to play with. We live next to a very busy street, and that's exactly where the hole was facing.
I immediately broke down and freaked out. I said a quick prayer and ran outside (fortunately this was not one of the days I decided to work in my bathrobe all day). I couldn't see her or hear her, but after a few minutes a car with a nice lady pulled over and asked if I was looking for a beagle. The lady had seen Lucy get out and run into the street, where apparently a large truck missed her by only a foot or so. The truck honked and scared Lucy into the other lane of traffic, where she had a few more close calls before running back into our subdivision. The woman pointed me a block over in the subdivision where Lucy was. I called her and she came quite quickly. She acted as if she knew she was in trouble but I didn't have the heart to punish her, I was just so glad she was alive! And it wasn't her fault- she didn't even dig the hole, she just wiggled through it. She doesn't know yet what fences are for.
The lady was nearly in tears, telling me over and over how lucky we were and how we nearly lost our dog forever.
Aside from that adventure, Lucy has had another struggle. Our dog, the most gentle and unintimidating dog ever, has taken to barking and growling at strangers. Mind you, Lucy does not bite- not even while playing, if you stick your hand it her mouth. You can poke your fingers in her food while she's eating and she still won't bite. But ever since we moved, she has become territorial of our house and barks and growls and bears her teeth at strangers. I hate it! I can't tell the people she's really a nice dog and won't bite- who'd believe it? The most I can do is punish her, and she's definitely been getting a lot of that lately. She flinches a lot now when we look at her the wrong way, because she's been in trouble so much lately. She's also had an upset stomach the whole time we've been here, though thankfully she waits til we take her outside.
And she really is so well trained! Go, stay, come, no bite, stand, attack mom, attack dad, wait, leave it, shake, up, down... she's got it all down. What can we do to show our new friends what a great dog she is? How could you not love this: