I'm an employment lawyer.
You really need to query why the role can't be done by 2 part timers. The definition of redundancy is - basically - a decline in work. This is not that, and so I'm not clear why there is a redundancy situation. If it was a role that could be done by one part time person and didn't require full time availability, it looks really odd that it can't be done by 2 part timers.
You are only entitled to claim redundancy as a type of unfair dismissal (or get a redundancy payment ) if you've been employed for more than 2 years. I assume this is the case from the info you have shared, but a claim for indirect sex discrimination (assuming you are a woman and have primary care commitments) doesn't require any length of service.
Are you certain this is genuine, and not some targettted way of getting rid of you for other reasons? It looks very very fishy. I would begin by challenging the fact that there is a redundancy situation at all because I don't think the legal test for that is met.
In terms of offering them a carrot, can you increase your hours/days a bit, but not work full time? It might help.
Defo contact your union if you are in one; also check car and house insurance because they often include legal cover as an extra.
I'd really advise challenging this though: 1) it is not a redundancy situation at all; 2) it is indirect sex discrimination. Put the above in a grievance.