Great advice from Saxon about crates etc and another vote from me about safe containment in the car. Interestingly our puppy stopped being sick as soon as I put him in a smaller crate - the first was too big for his puppy stage and the smaller one allowed him to brace against the sides whilst cornering (I should have bought this one sooner)!
Don't just take your pup to places, also consider short 'round the block' journeys too. I know that petrol is an issue, and it's not very
green going on unnecessary journeys but it is worth it in the long run. If you can load up the puppy and take a 10 minute trip it all helps to build up to the regular journeys you might need to do. I would take our puppy whenever I was collecting or dropping off the kids too and these 20 minute sessions did help. Plus, it also taught him that he always comes home again. You do just have to learn to shut your ears to the howling if your dog is that way inclined. For a time, mine would 'sing' all the way to training and all the way back again - dreadful. I'd just stick the radio on and sing too. The other advantage of short trips is that you know the whinging isn't caused by a full bladder. If you keep stopping 'cause you think she needs a wee you'll just teach her that all she has to do to make you stop and let her out is bark at you.
> Whats the best way on working on getting her to relax and enjoy the journey
I never found toys or chews were effective (at 12 months old he's still not interested in any in-crate entertainment I can provide) time and patience is all that's needed. From being a puking, howling, dribbling beastie he's now a great traveller. He just sleeps.
In the early days take kitchen roll and plastic bags for sickness and consider a non-slip but easily cleaned surface. Then just persevere, some dogs take to it faster than others. Good luck