I'm with @NorthernGirlie on this. Some school managements are shocking (and some are amazing, and you just wouldn't have this problem in those schools).
I had a similar thing happen to be (part-time teacher, expected to attend a meeting at short notice on my afternoon off). I refused to attend, head tried to put me on a disciplinary, but it turned out it was illegal for him to make me attend ANY meetings on my afternoon off.
The management are clearly a disorganised pile of shit, but will blame their uselessness on you. so leave ASAP, and because of the short notice, just don't attend the meeting, then get your union rep in if you have to. Remember management are probably getting paid quadruple what you're earning - their very job is to sort out these kinds of people issues, it's a basic management job. They crop up all the time in every school, and most HTs handle them in a kind and sensitive way.
And for goodness sakes stop stressing about it. If you don't have childcare due to short notice, then don't attend the meeting. Take control of your own life. Because the pay is so bad, some HLTAs have a second job, what would they do in that situation?
And I'm shocked by the number of PPs saying she should attend - even if she was a full-time teacher, I would question it in this situation, but she's just a HLTA on almost minimum wage. Why are so many of you colluding with the appalling management team? It's no wonder schools are in such a mess if poor management are actually supported and backed, instead of being called out for their uselessness. This problem has been caused by management, and they need to sort it out, not the OP. They have a duty of care, apart from anything.