It sounds like there is also so much other back story. While they shouldn't have had a go and it sounds like your mum has behaved awfully, I can imagine a situation where your DD is trying to tell you (badly) of her worried about your MH issues taking precedence in your life and overwhelming your ability to be part of the family or her mum, and this coming up. It's very unusual to leave a loved alone in a hospital like that, and I can imagine how it might play on your daughter's mind. She'd have to assume for her too, your anxiety about driving might be more real and urgent than your loved one's physical pain and fear, or risk of them dying alone. I have a family member like this, and when you realise they're not showing up, it's like a part of you dies.
(And this isn't just going in the ambulance, it's also about not driving, or calling your mother or a friend for a lift and/or staying with the teens, or taking a taxi).
You also haven't said why your DD might say that your DH is 'like a carer' for you on holiday. Is this down to the panic attacks that stop you driving or managing crowds and other mh issues?
Also I'm setting so many boundaries at work too that I am almost alone. Are you having issues there too?
Clearly they shouldn't take this approach, and if you have any access to counselling either as part of your MH treatment, though a work EAP programme or something else, you deserve and need support. They can also help work on boundaries whether that means cutting your mum off, or also adjusting boundaries if they're making you isolated at work, or not seeing your own DD's stress from being in a toxic situation. Noone should have to live like this, and I hope you can work your way through it.