Ok, here's my take based on what you've said already....
My first indication is that since you're constantly behind the aircraft, you have trouble with your scan. I assume that you're flying a 172 or something similar that has a standard six pack instrument setup. Here's the panel:
<IMG src="http://img34.exs.cx/img34/6950/panel.jpg" width=800>
I'm sure that your instructor has told you this already but it's worth repeating. Remember that your attitude indicator is your primary instrument. When you're doing different maneuvers other instruments become primary but I fly for the airlines and since I don't do steep turns, or the rest of those primary instrument training maneuvers anymore (expect in the simulator for pro checks anyway) the attitude indicator is primary. Start your scan there. Move back and forth from the attitude indicator, to the DG, back to the attitude indicator, over to the VSI, back to the attitude indicator, over to the altimeter, back to the attitude indicator, over to the airspeed indicator, back to the attitude indicator, over to the turn coordinator and again, back to the attitude indicator. Not necessarily in that order. But the idea is to have a constant scan going at all times. Remember that the attitude indicator is the ONLY instrument that gives you BOTH pitch and roll information. That's why it’s primary. None of the other five instruments give you both at the same time. Airspeed indicator gives pitch info, turn coordinator gives roll info, DG gives roll info, VSI gives pitch info, altimeter gives pitch info. The key is, to keep your scan going AT ALL TIMES. Don't stop scanning. Know what the instruments are telling you. Realize that some instruments can give you better info that others. For example, the VSI will help you to hold altitude better that just looking at the altimeter. Why? Because it's more sensitive to pitch changes. The aneroid wafers inside the altimeter lag a little bit where the VSI is hooked up directly to the static port on the side of the aircraft. Thereby, making it more sensitive.
It also sounds like you're disorganized in the cockpit. You say that you have two kneeboards, one for notes and one for approach plates. Do you have one of these? (Cat not included)

When I was instructing, I found that this yoke clip was very helpful because I didn't have to look all the way down to look at an approach plate. I still had a kneeboard though to copy down clearances when we would get a pop up clearance to do practice approaches.
Here are a couple of pointers on getting organized. An example for you, here's a sectional chart of my hometown, Anchorage, Alaska where I did my training and instructing:

Find Anchorage International and go northeast. See the white arrow? That's pointing to Merrill Field. My old airport. My point is that with my instrument students, we would depart from Merrill Field and file direct to Big Lake VOR which is an airport just southeast of the VOR (Big Lake VOR) at the top of the chart? See it? When we filed direct to the VOR we would go and shoot this approach:
<img src="http://img50.exs.cx/img50/8721/bgq.jpg" width=800>
Notice that this is a simple VOR approach. You're probably done one similar a few times already if you’re at that point yet. The point I'm getting at is how to organize the cockpit for this flight. I would have the VOR frequency (112.50) already dialed in the receiver so I wouldn't have to do it in the air. The DG is set to runway heading when you're on the centerline right before you apply power for takeoff. The approach plate is already in the holder ready to go so you don't have to dig it out enroute. Sitting on the runway, you are already talking to tower, and you should have departure control frequency set in the standby in the COM radio because that's who you'll be talking to once tower hands you off after takeoff. Do you see how you saved yourself a lot of work and you're not even off the ground yet? Once airborne, all you have to do is dial the OBS to center the needle and fly the heading that'll take you direct to the VOR. You have a good 20 minutes before you get there, plenty of time to brief the approach.
A point in copying clearances how's your shorthand? Remember there is no right or wrong way when using shorthand. As long as YOU can read it and (this is important) understand what you copied, then it's fine. Here's the clearance I would always get when flying from Merrill Field to Big Lake. (Remember, we filed direct and we always filed for 2000 feet.)
"Cessna 1234A, cleared to Big Lake airport as filed. Climb and maintain 2000. Departure control is on 119.1. Squawk 1234."
Here's my shorthand in how I always copied this clearance: (remember, this is my way you have to develop your own)
I think that it'll help if you get a yoke clip. That way you won't have to look down so much. When you do, you lose sight of the instruments and you mess up your scan.
I think that you do have to slow down. I had that problem when I was in your shoes. Take your time, think about what’s coming up next and get ready for it. It comes with practice.
Hopefully, this will help you a little.