Tl;dr at bottom, it got lengthy 

So about two years ago I ordered food on my phone from Panera Bread. I parked my car (within the lines) in the Togo parking spot that has a ten minute maximum. The parking lot was really full as it was lunch time and this place is right next to a military base. I go inside, make my drink, grab my bag and head back out. There’s a woman putting in her baby’s car seat in the spot next to mine and she is blocking my way to the driver door so I just stand and wait. After a few moments she hits my car with her door, but hey she’s got her hands full and my car has been through worse so I don’t say anything. She hit it a few times just trying to adjust the car seat and get it buckled correctly. Then she looks up and sees me waiting. She tells me essentially that I am not allowed to park next to her since she has a baby on board sticker and that it’s my fault she hit my door because I should have known that. I told her I didn’t pay attention to her car when I was parking and that she could’ve loaded her car from the other side (which was empty) or she could park farther away if she needs more room (she was directly in front of the door) and that since I’m in the lines and did not exceed my time I did absolutely nothing wrong. In the end she argued a bit, flipped me off and I grumbled “fuck you too, lady”. I’m not sure if she heard me or not. I know it was unnecessary to say that it was just me being angry at how entitled and snotty she was. 
I assumed that since the baby was fairly small she was just tired and grumpy overall. So AITA? Do people actually not park next to people who have those signs. I thought those were just for emergency services in case of a crash. It’s been two years and I still think about it whenever I see one. 

TL;DL: Lady says I should not of parked next to her because she had a “baby on board” sign and I was blocking her from fully opening her back door even though I was in my lines. We argue a little and she flips me off so I said “fuck you too” AITA? 