In reply to colin8ll:
You haven't explicitly written in a rest day. I would recommend at least one a week, both to avoid injury and keep the motivation firing, and to give you space to fit in other things in your life (I find I have rest days anyway, and scheduling them in makes me feel like I haven't messed up the programme!). Your comments about motivation and wee bugs are telling in this regard, the latter often arises as a result of over-training, and I used to suffer this a lot when ramping it up a lot suddenly.
I think most people do core at the end of their weights sessions, as you can train core on most days of the week since it recovers quite fast. Depends how much of a beasting of the core you have in mind I guess
Personally I try and challenge my core throughout weights sessions by using swiss ball instead of bench, and doing some sets of weights one-armed using a dumbbell where this makes sense : both habits I picked up from personal training.
You don't say how much you are currently doing, or what fitness level you are at, but if the answer is nowt then I think you will see improvements in all areas with your schedule. However, if it was me I'd probably aim for only 4 times a week (2 on, 1 off, 2 on, 2 off) but really aim to beast myself on those 4 days.
Btw I strongly recommend the book "Muscle" by Ian King (published in conjunction with Men's Health magazine) - it has lots of specific weights programmes at the back of the book. Actually Men's Health magazine itself has quite a lot of ideas for workouts in the back, and they've almost surely got a New Year's issue with lots of ideas.
Good luck! Andy