Aveline definitely does not have a motherly demeanor. Heck, Isabella acts more "motherly" than Aveline does.
Aveline is the first three things you mention: All about the spirit (and the letter, especially the letter) of the law, guard and protect. That seems to describe Cassandra to me.
Maybe it's because I only go off of what I see in games, not backstory, but I don't know about any traumatic childhood. I just know about a woman who's determined to do X to save her institution, just like Aveline does with the guard in Act's 1 and 3 (with the former captain).
Isabela motherly? We must have quite different mothers, mine surely never wanted to sleep with me. Aveline always seemed to be motherly to me: understanding, too helpful and always nagging me to keep in line.
When it comes to aggression nothing Aveline does in DA2 come close to what Cassandra do to Varric in the first few minutes by slamming a book in his face and stabbing a dagger in it. Cassandra is shown angry and screaming all through the prologue, Act 1 and Act 2. She even smirk after throwing the book in Varric's face, as if she likes scaring people. Aveline doesn't even like threatening a guy in DA2's prologue, but does it anyway because he deserved it.
Aveline being dedicated to the law and Cassandra being dedicated to the Chantry/Inquisition doesn't make them similar characters.
@StreetMagic
The Pentaghast are mentioned in Awakening Dragonspite bow and The Last Descent armor in DA2. They also have a few codex mention as well.