In the case of a baby old enough for finger foods, crying in very stop-slow traffic, DH should have got the baby out of the carseat and maybe the change of scenery and a change of entertainment would have been a distraction for her. He could have done more to prevent the upsetting screaming that caused you to make a poor decision.
More importantly and in general, I think it can be dangerous to drive with a din going on in the backseat that is upsetting and distracting to the driver. It doesn't matter how happy DH is with the noise. He is not the driver. If you are driving, then nobody second guesses your instructions to them or ignores your distress. Your preferences and factors that are affecting your driving are the only ones that matter. You and DH should sit down and discuss what happened, and you need to impress upon him that in future the driver pulls rank and everyone else says, 'Yes, sir" and does their utmost to deal with anything that might distract you.
I live and drive in the US and trips tend to be long, and I have five DCs to schlep around. The car is not a democracy. When we are out on the road, my word from the behind the steering wheel is the law. This makes for quiet passengers, a driver who is not distracted by noises, ball games, squabbling, bickering, out and out fights, or attention-seeking from the back seats, and safe trips.
Wrt the hard shoulder:
You can never tell if an additional emergency vehicle will roar up on the shoulder even if you think they have surely wound up their activities at a crash site.
And yyy to drowsy drivers drifting towards objects that are stationary, or just towards the side and sod's law, there you are.
In the case of breastfeeding babies, just take the baby out of the carseat and take care of it, then pop it back. Have done this myself on long trips when not driving, or on trips that turned out long (you do need to feed very young babies). No matter how young a baby, always bring an emergency bottle of water for it.