He could have parked in a disabled bay in that case?
Not every disabled person qualifies for a blue badge, no blue badge = no parking in the disabled bays.
Infants can go in pushchairs if you buy a pushchair that lies flat, most travel systems come with some sort of attachment (seat or carrycot) other than the carseat that a newborn can go in. Slings exist too. There are alternatives to removing the entire carseat and then schlepping it around the local shopping centre.
First off you would be handing over your baby to a complete stranger.
In non-covid times this is a non-issue. Stranger is highly unlikely to run off with your child especially if you choose your stranger wisely (e.g., elderly couple, parent with child of their own, carpark attendant, etc).
Just get the fuck on with it, park your car properly, pick up your baby and transport them around in the manner that best suits you. You are able bodied and need to pull yourself together
In the nicest possible way, pretty much this. At one time I had three DC under five then four under seven, I get that it can seem hard at times but there comes a point where you just need to get on with it because no one is going to do it for you. Instead of counting problems, look for solutions.