When a human cared jackdaw learns to fly it must be accepted by its original colony on the town square, but when a cruel politician hunts the colony into a cold forest, the jackdaw is being blamed and must rebuild trust to the town people so the colony can return home.  

No problem, happy to help!

The issue is that they make the square dirty and noisy - this isn't going to change if they return back there.

So the protagonist jackdaw ends up moving away from the colony? Where to? I think that if the story is about the jackdaw finding himself then maybe the Act I to II turn is actually him getting pushed out from the colony for getting them kicked out of their town square home. Then the jackdaw can spend act II struggling to find ways back in to the colony by trying to sort out a way for them to move back home, only to realise that he actually doesn't need the colony.

The B-Story is probably the relationship with the person who cared for him. I love the idea of this jackdaw returning back to this guy and trying to get a human's help to achieve his goal.

I'm a little confused. The jackdaw protagonist has to rebuild trust from the rest of the colony or the townspeople? If this politician has chased them out, why is he not just going to do that again? Surely in order to regain their home they must either get rid of the politician or do something for the townspeople to want them there. Do the jackdaws talk to each other? Do they talk to humans?

You say "must be accepted" - I would reserve "musts" for the goal. Since this has to happen for the story to happen and is fundamental to give us the goal, I would just go with "is accepted".

Why does the politician chase the colony away?

This is very wordy and there's a lot that can easily be trimmed. Why does it matter that this happens when the jackdaw learns to fly? Why is it a cold forest? "being blamed" can just be "blamed". Think about what is absolutely necessary to understand this story and ditch the rest. You're aiming for 35 words or less (fewer the better).

My biggest issue is that I just don't see how, once they've been kicked out, they can ever return back. Rebuilding trust doesn't automatically get their home back so even if they trust people again it doesn't mean anything. You've set the politician up as the antagonist - not people in general. So in order to get their home back they have to deal with this politician directly.

Why jackdaws? Just out of curiosity.