Tell your neighbour to soundproof her house. Keep the windows shut, whatever it takes. I'd be curious to know if she can hear them when they're inside too. At the end of the day you're doing the best you can to keep them happy. Some children are more demanding than others, you just drew a double short straw. You're not leaving the kids outside for hours while they cry, and if you don't want to leave your house every morning you shouldn't have to.