Yep, Hitler is a character in this book. He's surprisingly non-threatening, being characterized as "not a manly man" (1.3) who "loved his cakes" (1.3), and we might as well call him LLCoolA (Ladies Love Cool Adolf) because the babes go wild for him. They "baked him cakes [and] embroidered swastikas onto cushions and pillows for him" (24.176) like Nazi members of Etsy. (Etzi, if you will.) Knowing what we know about the real dude, it's all very strange to witness.
Ursula meets Hitler because she's friends with Eva, who likes taking pictures with her camera and doting on Ursula's daughter, Frieda. Ursula often wonders why they're together. Hitler has some sort of charisma that attracts Eva, even though he'd rather be married to Germany than to his lady love.
In one timeline, Ursula shoots Hitler. She uses her friendship with Eva to get close to him and, when he least expects it, pulls a gun on him and shoots him at close range. All his friends immediately shoot Ursula, so we have no idea just how this changes the course of the world. The narrative always dies with her.