some good advice from above.

definitely think honey needs to very gradually get used to being on her own at home. do you have a room in the house that you can leave her in when you go out? barkley relaxes much better if he's shut in the kitchen. it's become a routine that he is really familiar with. when we are going out, he gets a couple of biscuits, and is left with us calling 'bye, barkley, see you later!'. it's the routine we've followed since day one but obviously we always make sure he's been to the toilet and had a reasonable amount of exercise before we go, so he's happy to just snooze. and we started with leaving him for five minutes and built it up very gradually. you basically want honey to be completely confident that you WILL be back and a routine can really help with that, i think.

re: travelling in the car- agree with the advice about trying a crate. barkley was awful when we first took him out until we bought a crate, and put a comfy old duvet in the bottom. first trip in it, we put him in and just sat in the car for five minutes or so whilst he settled down, and he was asleep with two minutes of driving. also, if you put old towels in then it will be easier to clean up if she's sick.
good luck!