New weapons of the dynasty.

Go to the menu, specifically the dynasty section, give a pet to the hero you will be playing with, start a new game with that hero - PROFIT!

I tried it that way, I put the pet in the dynasty menu, selected that hero, started a Multiplayer game, but the pet was still inactive in the hero's menu. Maybe it's only for single-player.

...And is this by any chance a weapon from "The Shadow of Death"?

It's from "The Shadow of Death", although you can get it through a bug on the 4th map of Inferno. At least, I definitely found the Sword of Vengeance and the Unnamed Staff there. (I have the expansions installed, patch 2.1).

P.S. Please post screenshots of the following dynasty weapons:
********Swords
Sword of Vengeance
Blade of Balance

********Staffs
Unnamed Staff

And for completeness, here's the full list, as I thought, a total of 32... if anyone else finds anything else).

Swords:
1) Griffon Sword
2) Assassin's Blade
3) Blade of Chaos
4) Kirin's Silk Sword
5) Soul Eater
6) Perfect Silk Sword
7) Dragon's Fiery Tongue
8) Sword of Vengeance
9) Wolf Sword
10) Iron Feather
11) Pirate King's Sword
12) Alliance of Angels
13) Sword of Compulsion
14) Malatua's Cleaver
15) Arachne
16) Wiselbon's Sword
17) Blade of Balance

Staffs:
1) Staff of the Eight Aspects of Ashi
2) Oblivion
3) Staff of Purification
4) Staff of Sar-Aggreth
5) Sandro's Staff
6) Dragon Bone Staff
7) Sorrowful Song
8) Totem of Batu
9) Will of Urgash
10) Staff of Tides
11) Unnamed Staff
12) Staff of Thunder
13) Soul Stealer
14) Staff of Crystal Roses
15) Rod of the Underworld

Only 2 of the staffs from the list remain to be found, and then I'll have the complete set.