You poor thing! I had the opposite with my girls - the first was FUSSY like crazy, and the second was easy going. I found with my first that the snugli or sling or hug a bub or whatever carrier you want was a GREAT thing. Some fussy babies also like the swing (mine didn't - made her sea sick) I also used to lay her on a towel on the dryer when it was running sometimes, and the warm "rumblyness" seemed to soothe her.
As far as trying to "please" both your little ones, unfortunately, sometimes it's not possible. Lily is going to have to learn to wait for you, and that's not such a bad thing. It will help her to learn patience. But it won't be fun for a while. My older DD had the same issue when the younger one was born. It's a hard adjustment for them, but it is good for them to know that the world does not revolve around them. (I found that to be comforting to remember when I felt like I was "neglecting" her to take care of her little sister)
I'm sorry, I don't have a great solution for you, but it will not last forever, and I'm sure that by the time your DH has to go off for training, you'll be in a much better routine, and it will be OK. In the mean time, I would really recommend the sling for Charlie, and maybe a few little kids DVD's for Lily, for when things are really crazy, and if you can manage it, GET OUT by yourself for a little while! Get DH or someone to watch the kids and go for a walk or have a warm bath (with the door closed ) Relax your standards about everything else (ie. housework,etc.) or get help with that if you can, for a little while, and just work on getting through the day. It will be OK, you will make it!