I think you should run calibration and debayer (if OSC) on each night separately, and then register and integrate all images together.
To me it is the same process as integrating images from several nights of observing, each night with its own flats and dark flats.
I'm sure it is not the only way, possible not the best way either, but it works for me.
I don't know how comfortable you are with PI so I'll give you the steps.
Normally, using the defaults, WBPP script will calibrate, de-bayer (from a OSC camera), register and integrate your images to produce the final image. In your case you will need to use WBPP for the calibration and debayer functions but turn off the registration and Integration and do that separately.
First load into WBPP the first night of light, dark, flats, bias, whatever us normally use.
Go to the the lights tab of WBPP and deselect the Apply box of "image registration" and "image integration".
Then "run" as usual.
Do this again for the second night of data. Each nights data is done separately.
The WBPP output will be a set of debayered images with darks and flats and bias applied.
Now for both nights images you need to register them to line them up, and Integrate them all to get the final image.
Use process>StarAlignment for all the images, and then process>ImageIntegration to finish the workflow.
You should now have the finished image correctly calibrated and stacked.
Hope this helps.