Hi Georgina, I think it comes across as you intended. I'll add that I'm white and won't necessarily pickup up on unintentional messages. It's highly likely I'm not be as well informed as your Beta readers.
When I moved from London to a rural area in the early nineties, I noticed how many people were afraid of going to London even though it's within standard commuting distance (and many people do commute). The combination of a complicated transport system and the belief that Londoners were too unfriendly to help a stranger were huge barriers to going there unless you went as part of a coach trip. I also noticed how extremely racist rural people could be.
With all Cat's ongoing anxieties about her daughter I can see how she'd be nervous about everything. She comes across as fraught and inexperienced in a situation that's making her more paranoid than she'd normally be. The possibility of being asked a question when in London can be worrying if you think it will show up that you're a stranger and therefore vulnerable to any trick anyone wants to play on you. I think you've caught the perceptions of a well-meaning, anxious woman of 25 years ago who realises the mistake she's made and is very embarrassed.
I wasn't convinced that the social worker would behave in the way you portray him. I imagine he would know exactly why Cat was behaving as she does and wouldn't laugh as he'd know that could be taken as aggression. In my imagination of the scene he'd smile to reassure her but perhaps would also look sad or tired - or just something you as author could note for the reader even if Cat misses it. He'd also be well aware of the impression a large dog can have on someone nervous and how dogs have been used to control people, especially people from minorities. The dog didn't feel like a realistic character, as it were.
I don't know if this helps or not. At best it may break the scene down so that you can ask more questions of someone knowledgeable such as sensitivity reader.
As a general writing comment, the scene is pacey but currently tells a lot when, for me, it would be better to show more. I felt some sentences could be deleted, such as "Or is this it? .. the verge of hysterical giggling." In a moment of tension for Cat, less might be more.