Working hours issues

Need some advice for workplace hours if you don't mind.

Partner has worked at her place for over 10 years. Lately she went back from Maternity on agreed hours by both work and her.
Only few months later they decide those hours aren't suitable for them and ask her to change / shift her hours (start earlier finish later or vice versa) but she can't do that due to nursery run etc.
So she told them she can't do it, so they have taken hours off her claiming she has to be 'flexible', causing her to lose money.

Now bearing in mind, our lad goes school in September, so she has asked them can she work between school run, 9:30 2:30 as she will not be able to make it in for 9. They have basically flat out refused.

Here's the thing, there are other employees there, including the manager who rock up 'after 9' due to 'school run commitments'. Yet they won't budge for my Mrs at all. So she's gonna have to give her job up.

She is now about to hand her notice in.
Does she have a leg to stand on or is this just the way it is? I feel I know the answer.