This is seriously the world's most pathetic first world problem. It's a car park. Get over it (pwp, not disabled paeks). Seriously if you've got so little to worry about in your life that you are inspecting who parks in the pwp parks and are writing notes to leave on car windows then how about you just be grateful that that is your biggest worry in life.
I hate the things...they just cause unnecessary car park rage because apparently having a baby makes.you incapable of walking. If the pwp car parks are taken and it is a tight car parking lot with no room to make it safe to get the pram out then park further away and use the legs you were born with to walk. If someone parked there and they don't have kids then they maybe theu have a reason that marks the closer car park convenient for them, or maybe that just don't give a crap. Who freaking cares.....
OP yes it is fine to use the park if you're using a trolley and not a pram.
To those who have made popcorn and been waiting...you're welcome.
To those who are going to get their knickers in a knot and tell me I don't know what it is like I have three kids less than 4 years apaprt in age and was running all our errands, including a full grocery shop each week all on my own. I have spent so long getting my kids out of the car that the person who pulled in next to me after me had been to the shop, got what they wanted and left.again. I know what it is like.