Okay, I'm going to guess that you are new to sewing, so I'm going to try some basics *please* forgive me if this is stuff you're already doing!!
First thing that comes to mind is about the shrinking - you should wash your fabrics first, before you cut or sew. The thing about the fabric for fitteds is that they are absorbant, so not synthetic, they are supposed to shrink at the first wash! What I do is put all my yardage in my machine and send it through the same wash I do with my dipes. This also straightens out the weave of the fabric.
Okay, not sure about this, but if you are having any issues with the diaper 'warping' after you wash it, you might not be cutting your fabrics on the grain. You can rip the edges of a woven to get a straight edge (just snip with scissors and rip), then use the straight edges to make sure your pattern is on straight (measure from a fold line in the middle of the pattern to the edge at 2 places) or if you are putting a 1/2 pattern on a fold, just make sure you fold is straight. If you are using many layers, each one might be cut a little off and pulling at the shape of the diaper.
As for the fit issues, that's a tough one. This might not be the 'right' way, but if I was you, I would take a diaper I already own and like the fit of, then trace it onto wax paper (you might need DH to help stretch out the dipe), then add a seam allowance (just hold two markers together and trace the line). I'd take this wax paper and lay it over the VB
pattern and see what's going on. Then, I'd lay another piece of wax paper and trace the lines from each pattern that are working for your DD. The general shape and elastic placement should be closer to the VB
and I would think that all directions would still apply. This sounds complicated but it's not!
Okay, I have no idea what your cutting issues might be but if you are having serious problems and getting frustrated, you might try cutting just one layer (an outside layer) and get it just right, then just take rectangles of your other fabrics and lay them under and pin the heck out of them all... then sew all around, using the top piece as a guide, and cut the other layers to match afterward.
I really hope that helps with even a little bit of this!