Setting aside the voluntary bit for the moment: When a company restructures, they tend to draw up the org structure showing the roles they want to have in place by the end of the redundancy. There will be certain criteria they will want in certain roles, and in good companies they will split out the work into, for example "Admin roles - 4x full-time, or 8x part-time or equivalent mix thereof", and that means that being full/part time should only be relevant in terms of making sure the 'total' adds up to the work needed. However, 'need for flexibility for overtime' might be a criteria they put on a role (depends on the role itself and nature/culture of company) which could make you less attractive than other people under consideration. And of course if they only have one role planned, then they will decide if it is to be full-time OR part-time. Which doesn't mean that the role will automatically go to the person currently doing it full/part-time. They will decide who is best suited for the role and offer it to them first. that person can then accept or reject. If the role involves very substantial change in terms (eg switch from full- to part- time or vice versa) then the first person can reject it (and still potentially be eligible for redundancy) and the company can decide whether to offer it to the next in line. If there is no change in terms for the person they want to keep (eg full time person offered full time role) then the person is appointed automatically and the second is made redundant. The first person cannot refuse to do the role if it is the same as their current role - no-one can insist on being made redundant.
Offering a voluntary scheme means only that you wave a flag saying 'I'd prefer if it was me that was made redundant' and is a great way of matching up those you want to keep with those who want to be kept and vice versa. However, when all the eligible people offer themselves up for redundancy, it effectively negates the whole process of offering voluntary, and the firm then has to go back to first principles of choosing best candidate for the job (without excluding the 'voluntaries' first). So if you both offer yourselves up they will ignore that as a factor in the process,
In terms of should you stay or should you go, only you can answer that. I work in M&A and see the aftermath of large scale redundancies all the time. What I can say is that in general those who are left behind find the first 12 months or so very tough (more work, less people, combined with sometimes a huge drop in loyalty, especially amongst those who perceive that they or their colleagues or their departed colleagues have been unfairly treated). Sometimes redundancies offer an opportunity for people to leap out of boring roles into a faster career path in the same organisation (as a result of restructure), but IME it is often the hugely ambitious rather than the hugely talented that benefit. Things tend to settle down after around 18 months, but it will be a different organisation, with a different culture and a different atmosphere. Which of course could be a good thing.
As for the alternative of leaving, I have mentored people through this, and I tend to advise those who already have other job offers to jump ship (I don't advise that all the time - depends on the situation of course). If you think it would be difficult to find another job then I think you should sit tight and see what happens. It can be a huge boost to find that you are picked as preferred candidate against others (especially if you know that others are more flexible with overtime etc). And if you are not the preferred candidate then you will be made redundant anyway.
When you are thinking about all of this try to look at worst case scenarios and pick the one that sounds least bad.
I think your two choices of worst case are (1) you stay and they try to make you work longer hours and it is awful and you quit because of the stress, missing out on redundancy package you might have got, and (2) You leave, can't find another job, missing out on earnings and spending your redundancy before you find alternative work, and end up feeling a bit of a failure). Which sounds worst??
Sorry about your situation, by the way. A close friend of mine is in publishing and has been going through this for something like 15 years now. She works freelance now (which is ok but V stressful if you have a family to support)