On the legal front, shopping centres, as private property, are fully entitled to eject or bar anyone who parks in a space that the shopping centre has set aside for another type of customer.
There are some of these spaces in my local Tesco, but, even though there are security guards on patrol, they never enforce the rules. You frequently see people without kids in these spaces. Even worse, you often see commerical vehicles i.e. mini-vans, pick-ups etc. parked in these spaces. There should be more enforcement by the shopping centres.
I've shopped with young children, and sometimes you need one of these spaces. Especially if you've a young toddler, who isnt sure on feet yet, or a baby. People who dont need these spaces shouldnt use them full stop. If I'm shopping without kids, I'd never use one of these spots.
And its not just these spaces - in my local shopping centre, unauthorised people also park in the disabled spots and the taxi set-down area. Pure ignorance.