I know the conversation between your husband and the neighbour didn't go well, but once you have put your tactics in place to try and curb the crying/barking whilst you're at work, why not approach the neighbour again? In fact, I'd approach all of your neighbours. Explain that you have new pups, what you have done already to prevent the crying and the steps you are taking now. Agree with them that it can be hard with pups crying close by, but you're asking for their patience and understanding with what you're hoping to be short term problem. And most of all encourage them to let you know how it's going, so if it is getting really out of hand you can take other steps e.g. crated or kept inside, before you get hit with a council notice. Or they'll let you know when everything quietens down so you know they're right at home for the day.
I know it all sounds a bit much, but kill 'em with kindness! That's always been my theory, and I've always let neighbours know if we have a new dog to help get through that settling in period when they are first being left at home alone.
It might also help in the instance of if they aren't really crying that much, your other neighbours can back you up if the 'grumpy' neighbour really kicks up a stink. Good luck!