After reading all the replies, I'm kind of shocked I guess at some of the responses.
I'm not neglecting my child by letting her cry. I was trying to settle her whilst looking after my DS and push a trolley. I'm a fully functioning adult who can multi task. In the grand scheme of things, I felt in the moment it was better to get done and get home as quickly as possible.
My partner is not abusive, he works full time, he did not over react in my opinion but I know him, so I know that it's hard to portray that on here. He doesn't mistreat or disrespect waiting or service staff either.
I cannot keep stressing this enough, I don't want to complain about her actions, more raise it as a concern for the future. In my opinion she could have all the good intentions in the world, but she could actually harm someone. I am very lucky that my DS and DD are both in good health, no complications etc, but the fact is for me and my partner, this over stepped a boundary. Having worked for social care with families who have varying levels of needs, be them medical or social vulnerabilities, this could have major implications for someone who isn't confident enough to say anything.
I did say something, but I still felt like crap about having to hurt her feelings because she had good intentions. Imagine feeling so crap about asking someone to put down your baby that you get home and cry about it.
Im not young, I'm closer to to 40 than 30 and I consider myself a semi experienced parent with a lot of learning to do as they grow and hit new milestones and learn new things. I'm not daft, but for me this wasn't a case of its takes a village' 'accept all the help you can get' it was a 'my heart hit the floor because for a nanosecond I didn't know where my child was' moment. She was not where I, the parent, left her. I had control, I have been shopping god knows how many times and this was new. I panicked for a split second and that is not right. Parents should not be caused panic by a stranger whether it's their first child or their 21st child.
I respect all your opinions and points, I am aware that people have different views and styles of parenting and that is refreshing to know. I guess I've learnt more about me from this too.