Agree that its out of order, but its not really endangering her child and using that argument when its not true just switches people off.
If the neighbour won't talk to the OP, i would write a polite letter explaining why the OP objects to what's been done, clearly explain the rectification required, and ask for it to be dealt with amicably to avoid legal action.
If they still won't talk about it, then a solicitors letter and the threat of genuine legal action might be required. If that still doesn't work, i'd cut back the overhanging roof sheets and put up a section of guttering to direct the water back into their garden.