Double Planet Orbiting Wide Binary Star? Right now I'm writing a sci-fi story that develops in a double planet. But that's not all, the double planet (along with a couple more planets) orbit a big star and the whole system is orbited by another star (about 100 AU from the central star.)

I need to know how implausible this is. I don't want my story to drift from speculation into impossible worlds. I'm guessing that the occurrence of such a planetary arrangement is very low likely, but is such a system even possible at all? 

Now, if it's possible, how messed up the days and seasons would be? I'm bending my brain to figure out what would be the length of day and night in such a system (the planets are very close to each other.)

Any help with this will be really appreciated.
Generally speaking, there's 2 types of planet systems in a binary - see pretty picture.   Source.  The writer is a sci-fi writer so the entire article might be of interest to you.



Due to binary star tidal forces, there are some setups that are unlikely but in your example with a 100 AU distance between the stars, an orbit around the larger star is reasonable.

A double planet system is less likely.   It's unlikely to form on it's own during planet formation as that requires too much planetary angular momentum during formation.

It's possible, but also unlikely to form by giant impact, as that's more likely to leave 1 planet and 1 moon.  I've read (but can't find an article right now) that there's a giant impact size ratio and it's in the planet-moon range, not planet planet.   Much less than 1 to 1.  Pluto-Charon is 9-1 and Earth-Moon 81-1.   A giant impact is also unlikely to create an Iron rich core for both objects.   It's not a good way to create planet-planet.

That leaves a 3rd possibility, also unlikely, but perhaps the most likely of the bunch is planet capture.    Planets can form in Trojan points in the same orbit (Theia).  The difficulty with orbital capture is that the velocity needs to be just right and capture's are likely to be significantly elongated orbits, which, maybe, over time, perhaps with a 3rd asteroid, could even out to slightly more circular.   This is very improbable, but it might be the most likely way to form a double planet.

My 2 cents, as a layman.