I know - I hate it when people behave like this and it's really unforgivable in this situation when you've lined up childcare etc.

What d'you think you'll do - look for a different part-time job? I'd be inclined to explore all part-time options with them first because you can swap jobs down the track but I'm not sure there's that many good part-time jobs around.

I think it's still worth getting the legal advice. They've behaved really badly but don't let them bully you into resigning without exploring all your options first if your family budget relies on you working.