A new point of view, to help you cope with the guilt-trips,manipulation, and downright poisonous behaviour you're dealing with.
I personally think you'd be letting your sister down if you gave in now. If we take her stories at face value, we have a catalogue of irresponsibility.
*She didn't look after the birds- there was no water or food for them, and 12 died. They could have died from something else, but it's remarkably co-incidental, isn't it? At the very least, being hungry and thirsty doesn't help one's immune system fight off illness, does it? (How easy is it to recognise illness in birds, anyway? Would you and your husband say it's possible to recognise ill birds and call a vet?)
*Then, she apparently borrows an incredibly expensive piece of kit (the dock) from her friend. She forgets to collect the dock when she leaves.
*Then, she forgets to come back and get it for three months. And apparently has been fobbing off the owner all this time.
*She finally starts attempting to sort this all out in November. By which time, it is pretty impossible to sort out. Memories are faded, forensic linking and all that jazz are no longer possible, and if it's been sold on, it's long gone.
What will happen next if you pay for this one? She'll keep on acting like this, is what.
As you might be picking up, I knew a girl like this. I bet she still hasn't changed, either.