I am having trouble exercising a good roll when I start from a dive. I tend to roll towards my spine more than from shoulder to hip. It just seems impossible to roll more sideways while diving straight forwards.
I can do it, but it hurts more than jumping and rolling off a ten-foot wall.
I suspect that you're facing one of two problems.
When thinking of diving, the natural impulse is to dive straight forward, both arms outstretched, and execute a forward roll. This, naturally, draws you to roll across your spine, as it's the (literally) straightforward movement. To ensure rolling diagonally, you need to either dive at an angle (either from where you're facing or by twisting your torso while diving) or use your arms to guide your body into a diagonal movement. The latter is the more versatile option, but it puts more stress on your arms because they have to redirect your body weight. I advise setting up a video camera and taping yourself rolling (on a soft surface preferably). Look at how your torso is aligned as you're rolling. Also, Amos Rendao gives some good exercises to diagnose your rolling technique in part 1 of his intermediate parkour roll series (I highly recommend watching all four videos).
Are you trying to start your dive rolls from a standing position and launching yourself forward into a roll? Don't. Just like when you learned to roll initially, you need to employ progressions, starting from an all-fours position, moving up to leaning into it from standing and so on. This lets you ease into the movement rather than having to get it all right from full speed. Again, videotaping yourself is very handy to catch errors in technique.
You need to go to the opposite hip from the shoulder you land on. This roll or break fall (ukemi) is known as Mae Chugeri.
A very simple way to practice this is to take your lead arm, and make a 45 degree cutting movement down and across the front of your body; so if your left arm is forward then cut towards your right hip. Then allow your shoulder to follow the arm so that you end up in the roll.
If executed properly you should end up in the same stance as what you started in. This may be easier to start practicing from a kneeling stance (i.e. left leg bent, right knee on the floor).
This does mean that you will roll on a diagonal across your spine, but not down it. This roll is also ideal when executed while jumping or flying forwards.
For a good example of how to execute this, check this Youtube video, starting at 1:05.
In my old Aikido club we used to have people make a circle with their arms as if they were wrapping them around an exercise ball with the palms facing away. If you want to roll over right shoulder, you'd make the circle with your right elbow pointing up and right-hand fingers pointing down. If you want to roll over your left should, you'd make a circle with your left elbow pointing up and left-hand fingers pointing down. Remember that the palms should be turned away from you.
Begin training slowly by adopting the arm circle position and bending forward until your palms touch the ground. Once on the ground, the hand of the shoulder you want to roll over should have fingers pointing behind you. Tuck your head to the opposite side, away from the leading shoulder, as you roll. Contact with the ground should travel diagonally across your back as you roll, beginning with your leading shoulder. As you come out of the roll your feet should be turned sideways a bit so that you don't slam down on your heels.
After practicing this two-arm roll for a while you can begin rolling using just one arm, the arm of the leading shoulder, which as you initiate the roll should have elbow up, palm pointing away and fingers pointing down. But using two arms allows you to come in a steeper angle without collapsing the arms, and is a bit safer.
