Double Planet In A Wide Binary Star System

Right now I'm writing a sci-fi story that develops in a double planet (think of Rocheworld.) The double planet (along with a couple more planets) orbit a big star and the whole system is orbited by another star (about 10,000 AU from the central star.)

I need to know how implausible this is. I don't want my story to drift from speculation into the impossible. 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 days and seasons in this planet would be? I'm bending my brain to figure out what would be the length of day and night in such a system (since the planets are very close to each other.)

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Double Planet In A Wide Binary Star System

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