If Sedna orbited both Sol and "nemesis", it wouldn't have a possible orbit with Nemesis orbiting 848 AU out. A stable planetary orbit around two stars (circumbinary), is about a 1 to 5 ratio. The planet must be 5 times as far as the companion star. Sedna's perihelion is 76.361 AU. Using this information, let's do some simple calculations.
76/5 = 15.2 AU
Nemesis would have to orbit within about 15 AU for Sedna's perihelion to be so close. We'd obviously be able to see Nemesis (and if for some stupid reason we can't) we would feel the gravitational effects on other planets.
To put this into perspective, Saturn orbits near 9 AU and Uranus orbits at around 19. A mass that large would probably disturb Uranus so much, that it'd probably be thrown out of our solar system, which it obviously is not doing. And if Nemesis did orbit 848 AU, to throw Sedna back and forth between the sun and nemesis (while orbiting) would be nearly impossible every time, let alone once.