Just a little info for you..... They always make me take DD out of a sling/carrier to put the infant seatbelt on. They sometimes make me take the carrier off too, even if it's a HAB.
Does she like books? i find them a good distraction. I also sing with them, quietly! My singing might be bad, but it's better than them screaming. I also sometimes take a hand puppet for a bit of entertainment!