OP, the people criticising you are being unpleasant and silly.
I have a Blue Badge. There have been quite a few times where I have sat in the car, in a disabled space feeding DC3 (either before or after getting out of the car and going into shops/wherever). Usually takes about 10 minutes. She's older now, so I rarely need to do that any more.
But there are times where I check my phone for messages, fiddle about with the satnav to get it operational, turn around and give children in the back a stern talking to before we set off. Etc. etc. etc. I don't pull out of the parking space before I do any of those things.
(Actually I don't pull out of it at all, because my BB is for blindness, so it is DH who does the actual driving).
In order for your disabled children (who qualify for the BB) to go out and about, you as their carer must also care for your other children appropriately. If you could not do this, then your disabled children would never go anywhere.
Disability is a part of life, and people with disabilities need to live their lives. We need to be as considerate of others as anyone else. If you had a sensible option, I am sure you'd have moved your car a few yards to allow the other person to park. And that would have been kind of you, but not obligatory. But you didn't have that option. You did the best thing you could in the situation, and you should not be criticised for it in the slightest.
You sound like a lovely person, OP. I am really sad that you have been upset by this incident and some posters on this thread. I hope you can pay more attention to the (much larger number of) supportive voices. Your family deserve nice days out as much as any other, and the BB is there to help (in a very small way) with that.