Please don't think I'm trying to excuse shouty behaviour! I'm not at all.
I'm just thinking back to the years when I employed a nanny; there is a huge amount invested (emotionally) in employing someone to look after your children, and it can also be a very difficult balancing act, keeping your working hours to 9-5, so that you can be there when the nanny arrives, and then get home to let the nanny finish on time (and we were absolutely scrupulous about doing this), and getting your own work done/meetings attended, etc.
I was wondering whether, because of the miscommunication, it was possible that the employers thought that their own work arrangements (whatever they were) were now being compromised by the nanny not being available when they expected her to be.
I obviously have no idea if this is the case!
However, if you suddenly find out you can't do something/attend a meeting, etc, because you have no childcare, it can be very difficult, and very stressful, especially if it is short notice, and other peoples' schedules are also involved.
I can tell you, from my own experience, that the fear of having no-one to look after your child/children, when there's something really important that is going on at work is not an easy one to deal with, so I can understand why someone might lose it, if they thought that this was happening to them.
I'm not condoning it, but it makes it more understandable - in other words, there is a reason for their behaviour.
If there isn't a reason, then they are just bullies and the OP should find another job asap.
(And by the way, we had two nannies - the first one worked with us for 5 years and the second one for 9 years and we never raised our voices at either of them!
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