I only have a brief min to post. With regards to the bags - I personally would take them but on my terms and then follow through. So, you are helping her and not seen as unhelpful but you have some control so don't feel like a doormat. In other words - be reasonable.
I think in your sitch there is already too much anger; you don't need to exacerbate it.
So your points above - have you already said no? What have you said? (I am going out in about half an hour so can't reply after then) We can work out how to calm it down.
With regards to the children, have you worked it out officially or unofficially? You can say something like. 'I realise we are in the early stages of separation and working out the custody arrangements there are going to be some hitches along the way. How is it working for you?' Get her feedback - let her rant even. Then calmly say 'ok, well lets work out something we can both stick to consistently'. I get from you that she is taking the p a little at the moment with regards wanting you to babysit at the last min?? Is that correct?