Hi sassy, very impressed that you have managed to get out running already! 
Babies change so much in the first year. To start with our dt2 was laid back, and easy going, so dh took responsibility for him, and I would deal with dt1. Shortly after, he became the grumpy one and dh was lumbered! He stayed grumpy until he got moving - then he didn't stop!
It really sounds like she doesn't like being on her back, doesn't like the quiet, and all that will get easier as she gets older. Have you got an iphone/ipod/ipad? There are great apps available now which you can download for white noise to settle a baby, and it sounds like that might work for her. We used to leave a radio on static. I've def done the washing machine thing, and I promise they weren't still going to sleep in front of it at 6 months!
Having a preference for one side is also normal, and irrc you should have already had a check for their hips if they were born breach? If you are worried, ask your HV to have a look, they should be able to tell, but as far as I know, it isn't actually painful. She just sounds a bit grumpy, and your dt1 sounds very laid back in comparison, which might be making her look worse than she really is! I don't think at that age either of my dts were happy to lie awake for very long without being cuddled, rocked etc.
Once they get a bit older, you can get things like door bouncers, bumbos, stand in activity centers, and I bet dt2 wil be a lot happier!