KLM cancelled flight and transferred us to BA, who cancelled and transferred us to Air Berlin flight that was delayed. Where to claim compensation?

We were to fly from Milan (LIN) to Bergen (BGO) via Amsterdam (AMS). The flight were to depart from Milan 17:25, and we would arrive in Bergen 22:50.

The first flight got cancelled (two months before the travel), and we got new tickets were we would arrive the next day instead. This was followed by a rebookings after rebookings (we have had a total of 18 tickets for the return trip).

• 6 days before we were to travel from Milan, we got rescheduled to our original itinerary (but the first flight was operated by Alitalia instead of KLM).

• 3 days before we were to travel from Milan, we got rescheduled to a new route (LIN - LHR - AMS - BGO) departing Milan 13:20 (4 hours earlier than scheduled). I believe this should be enough to claim 2 x €400 in refund from KLM, according to EU's air passenger rights).

• British Airways had to cancel their flight to Heathrow (big IT-mess). We got help from KLM Customer Service and got a new itinerary: LIN - TXL - CPO - OSL - BGO, with an overnight stay in Copenhagen. The departure time was approximately the same as the original plan (but we got to the airport several hours earlier, to reach the plane to Heathrow).

Which airline(s) should we ask for a refund?

and how much can I get?

I thought I shoud ask KLM, since they got me the new tickets, and are the cause for the entire mess. The latest reschedule they made (before BA cancelled their flight was only three days prior to our departure).

We had to get a hotel room in Copenhagen.

KLM answered:

However, this cancellation happened well in advance and it was followed by several ticket reissues with other carriers.

[...] However, I need to explain that claims are dealt with by the flight operator, in this instance, British Airways for the cancellation of flight BA577 and Air Berlin due to the delay of their flight AB8735. Therefore, I can only recommend you to contact both carriers to proceed with your claim.

Note: Both my wife and our nanny lost almost a full day at work, incurring further expenses. Can we get a refund for this?