How do I avoid taking off the finish at the corners when sanding between coats?
A shop I worked at called this "burning the edge".  I was the noob and they never stopped smiling when it happened to me.  I was using toned lacquer, which was even more fragile.

Short Answer:

Sand near the edges by hand. Use a hard sanding block. Affix the sandpaper firmly. Go slow.  The flat level pressure should smooth the top plane without touching the side plane.

Long Answer:

You say you want to avoid rounding off your corners, but that's exactly what the surface tension of the finish is doing.  You always have a thinner coat at the edge of the corner.  Sanding off the same amount of material at the edge as the top will always result in a bald pinstripe and much hair pulling.  Sanding flat and level with a fine grit will smooth the top plane without touching the (inperceptively) round edge and make it appear sharper.

Try This Suggestion:

You're getting brush marks that you want to remove.  Have you tried thinning the finish before applying?  Use whatever thinner the product recommends and brush on thin coats.  Thin coats make thin brush marks and require only a light sanding before reapplying.  Always allow more drying time after each subsequent coat.

Good Luck!  You're not alone with this frustration.