Have you confirmed what your employee handbook/company policy and contract says yet?
I see you mentioned this is overtime, if I read that right. Technically they can't make you work overtime but if you don't you may lose the option to do it.
Keep it brief and to the point.
Main carer child, insufficient and unreasonable notice.
It's your choice next depending on whether these are contracted hours of overtime as to whether you want to work it or will be contractually required to.
What they can't do is dismiss you for it. Notice of the rota changing does not qualify as notice of the specific change unless they told you it would be Sunday. Furthermore this had to be in writing from them. Saying they told you 3 weeks ago for example is not acceptable.
As for how much notice they need to give you that can depend on a number of factors and your contract. The longest they would be required to serve a change in terms and conditions is 12 weeks. I suspect it will be as required or as per your contract notice in their terms and conditions/policy.
The problem is, you can fight it and you have considerable employee rights but; it costs time and money and unless they try to dismiss you or undertake a disciplinary, the outcome will be you, at some stage will need to work it (unless it's overtime and not contractual hours).
The key question here is what outcome do you actually want?
